By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose margina...By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product （IWOP） of Fermi operators is used in our discussion.展开更多
We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix repr...We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quan- tum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature.展开更多
The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks...The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks and the quantum channel capacity problems. In this paper, we primally introduce a notion of approximate private quantum channel (<em>ε</em>-PQC) on <em>fermionic</em> Gaussian systems (<em>i.e.</em>, <em>ε</em>-FPQC), and construct its explicit form of the fermionic (Gaussian) private quantum channel. First of all, we suggest a general structure for <em>ε</em>-FPQC on the fermionic Gaussian systems with respect to the Schatten <em>p</em>-norm class, and then we give an explicit proof of the statement in the trace norm case. In addition, we study that the cardinality of a set of fermionic unitary operators agrees on the <em>ε</em>-FPQC condition in the trace norm case. This result may give birth to intuition on the construction of emerging fermionic Gaussian quantum communication or computing systems.展开更多
From resolving Klein-Gordon equation and Dirac equation in (2+1)-dimensional charged black hole spacetime and using 't Hooft's boundary condition and "quasi-periodic" boundary condition in the thin f...From resolving Klein-Gordon equation and Dirac equation in (2+1)-dimensional charged black hole spacetime and using 't Hooft's boundary condition and "quasi-periodic" boundary condition in the thin film brick wall model of black hole, which is introduced by LIU Weng-Biao and ZHAO Zheng, we obtain the bosonic and fermionic entropy of (2+1)-dimensional charged black hole, and find that the bosonic entropy is three times of fermionic entropy.展开更多
The central extension of the (1+1)-dimensional Poincaré algebra by including fermionic charges which obey not supersymmetric algebra, but a special graded algebra containing in the right hand side a central eleme...The central extension of the (1+1)-dimensional Poincaré algebra by including fermionic charges which obey not supersymmetric algebra, but a special graded algebra containing in the right hand side a central element only is obtained. The corresponding theory being the fermionic extension of the lineal gravity is proposed. We considered the algebra of generators, the field transformations and found Lagrangian and equation of motion, then we derived the Casimir operator and obtained the con- stant black hole mass.展开更多
Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi ar...Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.展开更多
Based on the algebraic entanglement measure proposed [G. Vidal et al., Phys. Rev. A 65 (2002) 032314],we study the entanglement evolution of both pure quantum states and mixed ones of 2-qutrit system in a symmetrybrok...Based on the algebraic entanglement measure proposed [G. Vidal et al., Phys. Rev. A 65 (2002) 032314],we study the entanglement evolution of both pure quantum states and mixed ones of 2-qutrit system in a symmetrybroken environment consisting of a fermionic bath. Entanglement of states will decrease or remain constant under the influence of environment, and the class of states which remain unchanged has been found out.展开更多
We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in （5＋1） dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure...We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in （5＋1） dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.展开更多
We study the superfuild ground state of ultracold fermions in optical lattices with a quadratic band touching. Examples are a checkerboard lattice around half filling and a kagome lattice above one third filling. Inst...We study the superfuild ground state of ultracold fermions in optical lattices with a quadratic band touching. Examples are a checkerboard lattice around half filling and a kagome lattice above one third filling. Instead of pairing between spin states, here we focus on pairing interactions between different orbital states. We find that our systems have only odd-parity （orbital） pairing instability while the singlet （orbital） pairing instability vanishes thanks to the quadratic band touching. In the mean field level, the ground state is found to be a chiral p-wave pairing superfluid （mixed with finite f-wave pairing order-parameters） which supports Majorana fermions.展开更多
In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two-dimensional compact manifold S2 as extra dimensions. The result is that there exist massless Dirac fermions which have normali...In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two-dimensional compact manifold S2 as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the sphere axe discussed and some simple fermionic zero modes are obtained.展开更多
The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the mult...The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the multidimen- sional super integrable equation and investigate its Lax representation. Furthermore, the Backlund transformation is presented and we derive a solution to the super integrable equation.展开更多
We want to show extra-dimensions corrections for Fermionic Casimir Effect. Firstly, we determined quantization fermion field in Three dimensional Box. Then we calculated the Casimir energy for massless fermionic field...We want to show extra-dimensions corrections for Fermionic Casimir Effect. Firstly, we determined quantization fermion field in Three dimensional Box. Then we calculated the Casimir energy for massless fermionic field confined inside a three-dimensional rectangular box with one compact extra-dimension. We use the MIT bag model boundary condition for the confinement and M4 × S1 as the background spacetime. We use the direct mode summation method along with the Abel-Plana formula to compute the Casimir energy. We show analytically the extra-dimension corrections to the Fermionic Casimir effect to forward a new method of exploring the existence of the extra dimensions of the universe.展开更多
We study the phase diagram of the interacting fermionic two-leg ladder, which is featured by pair hopping and interactions of singlet and triplet superconducting channels. By using Abelian bosonization method, we obta...We study the phase diagram of the interacting fermionic two-leg ladder, which is featured by pair hopping and interactions of singlet and triplet superconducting channels. By using Abelian bosonization method, we obtain the full phase diagram of our model. The superconducting triplet pairing phase is characterized by a fractional edge spin and interpreted as two Kitaev chains under the mean filed approximation. The pair hopping will give rise to spin-density-wave(SDW)orders and can also support Majorana edge modes in spin channel. At half filling, the resulting Majorana-SDW phase shows additional fractionalization in charge channel, and can be interpreted as two Su–Schrieffer–Heeger(SSH) chains in the mean field regime.展开更多
Oxygenations are highly exergonic, yet combustion of organic matter is not spontaneous in an atmosphere that is 21% O<sub>2</sub>. Electrons are fermions with a quantum spin number<em> s</em> o...Oxygenations are highly exergonic, yet combustion of organic matter is not spontaneous in an atmosphere that is 21% O<sub>2</sub>. Electrons are fermions with a quantum spin number<em> s</em> of 1/2<span style="white-space:nowrap;"><em><span style="white-space:nowrap;">ħ</span></em></span>. An orbital containing a single electron with <em>s</em> = 1/2 is fermionic. Orbitals can contain a maximum of two electrons with antiparallel spins,<em> i.e.</em>, spin magnetic quantum numbers <em>m</em><sub><em>s</em></sub> of 1/2 and -1/2. An orbital filled by an electron couple has <em>s</em> = 0 and bosonic character. The multiplicity of a reactant is defined as |2(<em>S</em>)| + 1 where <em>S</em> is the total spin quantum number. The Wigner spin conservation rules state that multiplicity is conserved. The transmission coefficient <em>κ</em> of absolute reaction rate theory also indicates the necessity for spin conservation. Burning is fermionic combustion that occurs when sufficient energy is applied to a bosonic molecule to cause homolytic bond cleavage yielding fermionic products capable of reaction with the bifermionic frontier orbitals of triplet multiplicity O<sub>2</sub>. Neutrophil leucocytes kill microorganisms by bosonic combustion and employ two mechanisms for changing the multiplicity of O<sub>2</sub> from triplet to singlet. Microorganisms, composed of bosonic singlet multiplicity molecules, do not directly react with bifermionic O<sub>2</sub>, but are highly susceptible to electrophilic attack by bosonic electronically excited singlet molecular oxygen (<span style="white-space:nowrap;"><sup>1</sup>O<sub>2</sub><sup style="margin-left:-10px;">*</sup></span><span style="font-size:10px;white-space:nowrap;">).</span> Hydride ion (H<sup>-</sup>) transfer is the common mode of cytoplasmic redox metabolism. Bosonic transfer of an orbital electron couple protects from damage by obviating fermionic reaction with bifermionic O<sub>2</sub>. Bosonic coupled electron transfer raises the consideration that quantum tunneling might be involved in facilitating such redox transfer.展开更多
We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line P[r].Furthermore,we deduce the explicit bilinear Fermionic formula for the(stationary...We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line P[r].Furthermore,we deduce the explicit bilinear Fermionic formula for the(stationary)Gromov-Witten potential via the lifting operator contructed from the Baker-Akhiezer function.展开更多
Majorana zero modes(MZMs)have been intensively studied in recent decades theoretically and experimentally as the most promising candidate for non-Abelian anyons supporting topological quantum computation(TQC).In addit...Majorana zero modes(MZMs)have been intensively studied in recent decades theoretically and experimentally as the most promising candidate for non-Abelian anyons supporting topological quantum computation(TQC).In addition to the Majorana scheme,some non-Majorana quasiparticles obeying non-Abelian statistics,including topological Dirac fermionic modes,have also been proposed and therefore become new candidates for TQC.In this review,we overview the non-Abelian braiding properties as well as the corresponding braiding schemes for both the MZMs and the topological Dirac fermionic modes,emphasizing the recent progress on topological Dirac fermionic modes.A topological Dirac fermionic mode can be regarded as a pair of MZMs related by unitary symmetry,which can be realized in a number of platforms,including the one-dimensional topological insulator,higher-order topological insulator,and spin superconductor.This topological Dirac fermionic mode possesses several advantages compared with its Majorana cousin,such as superconductivity-free and larger gaps.Therefore,it provides a new avenue for investigating non-Abelian physics and possible TQC.展开更多
We synthesize high-quality single crystal of CeGaSi by a Ga self-flux method and investigate its physical properties through magnetic susceptibility,specific heat and electrical resistivity measurements as well as hig...We synthesize high-quality single crystal of CeGaSi by a Ga self-flux method and investigate its physical properties through magnetic susceptibility,specific heat and electrical resistivity measurements as well as high pressure effect.Magnetic measurements reveal that an antiferromagnetic order develops below T_(m)~10.4 K with magnetic moments orientated in the ab plane.The enhanced electronic specific heat coefficient and the negative logarithmic slope in the resistivity of CeGaSi indicate that the title compound belongs to the family of Kondo system with heavy fermion ground states.The max magnetic entropy change-ΔS_(M)^(max)(μ_(0)H⊥c,μ_(0)H=7 T) around T_(m) is found to reach up to 11.85 J·kg^(-1)·K^(-1).Remarkably,both the antiferromagnetic transition temperature and-ln T behavior increase monotonically with pressure applied to 20 kbar(1 bar=10~5 Pa),indicating that much higher pressure will be needed to reach its quantum critical point.展开更多
The combination of non-Hermitian physics and Majorana fermions can give rise to new effects in quantum transport systems. In this work, we investigate the interplay of PT-symmetric complex potentials, Majorana tunneli...The combination of non-Hermitian physics and Majorana fermions can give rise to new effects in quantum transport systems. In this work, we investigate the interplay of PT-symmetric complex potentials, Majorana tunneling and interdot tunneling in a non-Hermitian double quantum dots system. It is found that in the weak-coupling regime the Majorana tunneling has pronounced effects on the transport properties of such a system, manifested as splitting of the single peak into three and a reduced 1/4 peak in the transmission function. In the presence of the PT-symmetric complex potentials and interdot tunneling, the 1/4 central peak is robust against them, while the two side peaks are tuned by them. The interdot tunneling only induces asymmetry, instead of moving the conductance peak, due to the robustness of the Majorana modes. There is an exceptional point induced by the union of Majorana tunneling and interdot tunneling. With increased PT-symmetric complex potentials, the two side peaks will move towards each other. When the exceptional point is passed through, these two side peaks will disappear. In the strong-coupling regime, the Majorana fermion induces a 1/4 conductance dip instead of the three-peak structure. PT-symmetric complex potentials induce two conductance dips pinned at the exceptional point. These effects should be accessible in experiments.展开更多
Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism ...Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism which is proportional to Planck’s constant. This may be the result of two massless bosons (hypergluons) coupled by a preon (prequark) exchange. It also gives a physical explanation to the origin of the Planck constant, and origin of spin.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475056 and 10574060
文摘By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product （IWOP） of Fermi operators is used in our discussion.
基金supported by the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province+1 种基金China(Grant Nos.ZR2013AM012 and ZR2012AM004)the Research Fund for the Doctoral Program and Scientific Research Project of Liaocheng University,Shandong Province,China
文摘We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quan- tum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature.
文摘The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks and the quantum channel capacity problems. In this paper, we primally introduce a notion of approximate private quantum channel (<em>ε</em>-PQC) on <em>fermionic</em> Gaussian systems (<em>i.e.</em>, <em>ε</em>-FPQC), and construct its explicit form of the fermionic (Gaussian) private quantum channel. First of all, we suggest a general structure for <em>ε</em>-FPQC on the fermionic Gaussian systems with respect to the Schatten <em>p</em>-norm class, and then we give an explicit proof of the statement in the trace norm case. In addition, we study that the cardinality of a set of fermionic unitary operators agrees on the <em>ε</em>-FPQC condition in the trace norm case. This result may give birth to intuition on the construction of emerging fermionic Gaussian quantum communication or computing systems.
文摘From resolving Klein-Gordon equation and Dirac equation in (2+1)-dimensional charged black hole spacetime and using 't Hooft's boundary condition and "quasi-periodic" boundary condition in the thin film brick wall model of black hole, which is introduced by LIU Weng-Biao and ZHAO Zheng, we obtain the bosonic and fermionic entropy of (2+1)-dimensional charged black hole, and find that the bosonic entropy is three times of fermionic entropy.
文摘The central extension of the (1+1)-dimensional Poincaré algebra by including fermionic charges which obey not supersymmetric algebra, but a special graded algebra containing in the right hand side a central element only is obtained. The corresponding theory being the fermionic extension of the lineal gravity is proposed. We considered the algebra of generators, the field transformations and found Lagrangian and equation of motion, then we derived the Casimir operator and obtained the con- stant black hole mass.
基金Climb-Up (Pan Deng) Project of Department of Science and Technology of China，国家自然科学基金，Doctoral Programme Foundation of Institution of Higher Education of China
文摘Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.
文摘Based on the algebraic entanglement measure proposed [G. Vidal et al., Phys. Rev. A 65 (2002) 032314],we study the entanglement evolution of both pure quantum states and mixed ones of 2-qutrit system in a symmetrybroken environment consisting of a fermionic bath. Entanglement of states will decrease or remain constant under the influence of environment, and the class of states which remain unchanged has been found out.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10275030 and 10475034 and the Fundamental Research Fund for Physics and Mathematics of Lanzhou University （No. lzu0702）
文摘We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in （5＋1） dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant No.11675116)the Soochow University,China
文摘We study the superfuild ground state of ultracold fermions in optical lattices with a quadratic band touching. Examples are a checkerboard lattice around half filling and a kagome lattice above one third filling. Instead of pairing between spin states, here we focus on pairing interactions between different orbital states. We find that our systems have only odd-parity （orbital） pairing instability while the singlet （orbital） pairing instability vanishes thanks to the quadratic band touching. In the mean field level, the ground state is found to be a chiral p-wave pairing superfluid （mixed with finite f-wave pairing order-parameters） which supports Majorana fermions.
基金National Natural Science Foundation of China under Grant Nos.10475034 and 10705013the Fundamental Research Fund for Physics and Mathematics of Lanzhou University under Grant No.Lzu07002
文摘In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two-dimensional compact manifold S2 as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the sphere axe discussed and some simple fermionic zero modes are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11605096,11547101 and 11601247
文摘The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the multidimen- sional super integrable equation and investigate its Lax representation. Furthermore, the Backlund transformation is presented and we derive a solution to the super integrable equation.
文摘We want to show extra-dimensions corrections for Fermionic Casimir Effect. Firstly, we determined quantization fermion field in Three dimensional Box. Then we calculated the Casimir energy for massless fermionic field confined inside a three-dimensional rectangular box with one compact extra-dimension. We use the MIT bag model boundary condition for the confinement and M4 × S1 as the background spacetime. We use the direct mode summation method along with the Abel-Plana formula to compute the Casimir energy. We show analytically the extra-dimension corrections to the Fermionic Casimir effect to forward a new method of exploring the existence of the extra dimensions of the universe.
基金Project supported by the Open Project of the State Key Laboratory of Surface Physics in Fudan University,China(Grant No.KF2018_13)the Ph.D. Research Startup Foundation of Anhui University(Grant No.J01003310)
文摘We study the phase diagram of the interacting fermionic two-leg ladder, which is featured by pair hopping and interactions of singlet and triplet superconducting channels. By using Abelian bosonization method, we obtain the full phase diagram of our model. The superconducting triplet pairing phase is characterized by a fractional edge spin and interpreted as two Kitaev chains under the mean filed approximation. The pair hopping will give rise to spin-density-wave(SDW)orders and can also support Majorana edge modes in spin channel. At half filling, the resulting Majorana-SDW phase shows additional fractionalization in charge channel, and can be interpreted as two Su–Schrieffer–Heeger(SSH) chains in the mean field regime.
文摘Oxygenations are highly exergonic, yet combustion of organic matter is not spontaneous in an atmosphere that is 21% O<sub>2</sub>. Electrons are fermions with a quantum spin number<em> s</em> of 1/2<span style="white-space:nowrap;"><em><span style="white-space:nowrap;">ħ</span></em></span>. An orbital containing a single electron with <em>s</em> = 1/2 is fermionic. Orbitals can contain a maximum of two electrons with antiparallel spins,<em> i.e.</em>, spin magnetic quantum numbers <em>m</em><sub><em>s</em></sub> of 1/2 and -1/2. An orbital filled by an electron couple has <em>s</em> = 0 and bosonic character. The multiplicity of a reactant is defined as |2(<em>S</em>)| + 1 where <em>S</em> is the total spin quantum number. The Wigner spin conservation rules state that multiplicity is conserved. The transmission coefficient <em>κ</em> of absolute reaction rate theory also indicates the necessity for spin conservation. Burning is fermionic combustion that occurs when sufficient energy is applied to a bosonic molecule to cause homolytic bond cleavage yielding fermionic products capable of reaction with the bifermionic frontier orbitals of triplet multiplicity O<sub>2</sub>. Neutrophil leucocytes kill microorganisms by bosonic combustion and employ two mechanisms for changing the multiplicity of O<sub>2</sub> from triplet to singlet. Microorganisms, composed of bosonic singlet multiplicity molecules, do not directly react with bifermionic O<sub>2</sub>, but are highly susceptible to electrophilic attack by bosonic electronically excited singlet molecular oxygen (<span style="white-space:nowrap;"><sup>1</sup>O<sub>2</sub><sup style="margin-left:-10px;">*</sup></span><span style="font-size:10px;white-space:nowrap;">).</span> Hydride ion (H<sup>-</sup>) transfer is the common mode of cytoplasmic redox metabolism. Bosonic transfer of an orbital electron couple protects from damage by obviating fermionic reaction with bifermionic O<sub>2</sub>. Bosonic coupled electron transfer raises the consideration that quantum tunneling might be involved in facilitating such redox transfer.
基金Supported by National Key R&DProgram of China(Grant No.2020YFE0204200)NSFC(Grant Nos.12225101,12061131014 and 11890660)。
文摘We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line P[r].Furthermore,we deduce the explicit bilinear Fermionic formula for the(stationary)Gromov-Witten potential via the lifting operator contructed from the Baker-Akhiezer function.
基金financially supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302400)the National Natural Science Foundation of China(Grant No.11974271)+2 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)the National Basic Research Program of China(Grant No.2015CB921102)the China Postdoctoral Science Foundation(Grant No.2021M690233)。
文摘Majorana zero modes(MZMs)have been intensively studied in recent decades theoretically and experimentally as the most promising candidate for non-Abelian anyons supporting topological quantum computation(TQC).In addition to the Majorana scheme,some non-Majorana quasiparticles obeying non-Abelian statistics,including topological Dirac fermionic modes,have also been proposed and therefore become new candidates for TQC.In this review,we overview the non-Abelian braiding properties as well as the corresponding braiding schemes for both the MZMs and the topological Dirac fermionic modes,emphasizing the recent progress on topological Dirac fermionic modes.A topological Dirac fermionic mode can be regarded as a pair of MZMs related by unitary symmetry,which can be realized in a number of platforms,including the one-dimensional topological insulator,higher-order topological insulator,and spin superconductor.This topological Dirac fermionic mode possesses several advantages compared with its Majorana cousin,such as superconductivity-free and larger gaps.Therefore,it provides a new avenue for investigating non-Abelian physics and possible TQC.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12274440)the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB33010100)+1 种基金the Fund from the Ministry of Science and Technology of China (Grant No. 2022YFA1403903)the Fund of the Synergetic Extreme Condition User Facility (SECUF)。
文摘We synthesize high-quality single crystal of CeGaSi by a Ga self-flux method and investigate its physical properties through magnetic susceptibility,specific heat and electrical resistivity measurements as well as high pressure effect.Magnetic measurements reveal that an antiferromagnetic order develops below T_(m)~10.4 K with magnetic moments orientated in the ab plane.The enhanced electronic specific heat coefficient and the negative logarithmic slope in the resistivity of CeGaSi indicate that the title compound belongs to the family of Kondo system with heavy fermion ground states.The max magnetic entropy change-ΔS_(M)^(max)(μ_(0)H⊥c,μ_(0)H=7 T) around T_(m) is found to reach up to 11.85 J·kg^(-1)·K^(-1).Remarkably,both the antiferromagnetic transition temperature and-ln T behavior increase monotonically with pressure applied to 20 kbar(1 bar=10~5 Pa),indicating that much higher pressure will be needed to reach its quantum critical point.
基金Project supported by the National Natural Science Foundation of China (Grant No.11834005)。
文摘The combination of non-Hermitian physics and Majorana fermions can give rise to new effects in quantum transport systems. In this work, we investigate the interplay of PT-symmetric complex potentials, Majorana tunneling and interdot tunneling in a non-Hermitian double quantum dots system. It is found that in the weak-coupling regime the Majorana tunneling has pronounced effects on the transport properties of such a system, manifested as splitting of the single peak into three and a reduced 1/4 peak in the transmission function. In the presence of the PT-symmetric complex potentials and interdot tunneling, the 1/4 central peak is robust against them, while the two side peaks are tuned by them. The interdot tunneling only induces asymmetry, instead of moving the conductance peak, due to the robustness of the Majorana modes. There is an exceptional point induced by the union of Majorana tunneling and interdot tunneling. With increased PT-symmetric complex potentials, the two side peaks will move towards each other. When the exceptional point is passed through, these two side peaks will disappear. In the strong-coupling regime, the Majorana fermion induces a 1/4 conductance dip instead of the three-peak structure. PT-symmetric complex potentials induce two conductance dips pinned at the exceptional point. These effects should be accessible in experiments.
文摘Using real fields instead of complex ones, it is suggested here that the fermions are pairs of coupled strings with an internal tension. The interaction between the two coupled strings is due to an exchange mechanism which is proportional to Planck’s constant. This may be the result of two massless bosons (hypergluons) coupled by a preon (prequark) exchange. It also gives a physical explanation to the origin of the Planck constant, and origin of spin.
