The note gives a watertight confirmation of the E-infinity Cantorian theory results for ordinary and dark cosmic energy density of the universe and respectively. The computation is fundamentally based on a golden mean...The note gives a watertight confirmation of the E-infinity Cantorian theory results for ordinary and dark cosmic energy density of the universe and respectively. The computation is fundamentally based on a golden mean fusion function that goes back to the highly original anyon proposal of F. Wilczek.展开更多
Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore–Read fractional quantum Hall state. Its quasihole states are zero-ener...Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore–Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore–Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.展开更多
We show that it is possible to simulate an anyon by a trapped atom which possesses an induced electric dipole moment in the background of electric and magnetic fields in a specific configuration.The electric and magne...We show that it is possible to simulate an anyon by a trapped atom which possesses an induced electric dipole moment in the background of electric and magnetic fields in a specific configuration.The electric and magnetic fields we applied contain a magnetic and two electric fields.We find that when the atom is cooled down to the limit of the negligibly small kinetic energy,the atom behaves like an anyon because its angular momentum takes fractional values.The fractional part of the angular momentum is determined by both the magnetic and one of the electric fields.Roles electric and magnetic fields played are analyzed.展开更多
A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such...A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as super-symmetric quantum mechanics,super-symmetric gravity,super-symmetric string theory,super-symmetric integrable systems and so on.Supersymmetry and Grassmann numbers are,in some sense,dual conceptions,and it turns out that these conceptions coincide for the ren situation,that is,a similar conception of ren-number(R-number)is devised for ren-symmetry.In particular,some basic results of the R-number and ren-symmetry are exposed which allow one to derive,in principle,some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems.Training examples of ren-integrable KdV-type systems and ren-symmetric KdV equations are explicitly given.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 study quantum classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the ...We study quantum classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than h is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 27r-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.展开更多
We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, suc...We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, such as the Ising model,Hamiltonian model of quantum Hall effect, fermion pairing model, Kitaev honeycomb lattice model, and so on, are the short-range coupling cases of this knot lattice model. The long-range coupling knot lattice model bears Abelian and nonAbelian anyons, and shows integral and fractional filling states like the quantum Hall system. The fusion rules of anyons are explicitly demonstrated by braiding crossing states. The eigenstates of quantum models can be represented by a multilayer link lattice pattern whose topology is characterized by the linking number. This topological linking number offers a new quantity to explain and predict physical phenomena in conventional quantum models. For example, a convection flow loop is introduced into the well-known Bardeen–Cooper–Schrieffer fermion pairing model to form a vortex dimer state that offers an explanation of the pseudogap state of unconventional superconductors, and predicts a fractionally filled vortex dimer state. The integrally and fractionally quantized Hall conductance in the conventional quantum Hall system has an exact correspondence with the linking number in this multi-knot lattice model. The real-space knot pattern in the topological insulator model has an equivalent correspondence with the Lissajous knot in momentum space. The quantum phase transition between different quantum states of the quantum spin model is also directly quantified by the change of topological linking number, which revealed the topological character of phase transition. Circularized photons in an optical fiber network are a promising physical implementation of this multi-knot lattice, and provide a different path to topological quantum computation.展开更多
The dynamics of neutral spinning particles in electromagnetic fields is investigated. The phase interference of unpolarized neutron beams is reasonably interpreted as the observed spin precession in external fields in...The dynamics of neutral spinning particles in electromagnetic fields is investigated. The phase interference of unpolarized neutron beams is reasonably interpreted as the observed spin precession in external fields instead of potential effects in the quantum physics; namely, the Aharonov-Bohm and Aharonov-Casher effects. It is also pointed out that the recent experiment claimed to be the verification of Aharonov-Casher phase with neutron interferometry, however, can be considered as a test of new anyon model.展开更多
We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that th...We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.展开更多
<正> By using the gauge-invariance,a Klein-Gordon’s type equation for anyons in external fields is constructed.The equation can be solved exactly in a constant electric and magnetic field,as well as in a quanti...<正> By using the gauge-invariance,a Klein-Gordon’s type equation for anyons in external fields is constructed.The equation can be solved exactly in a constant electric and magnetic field,as well as in a quantized electromagnetic field.The analytic forms of solutions are also given in detail.展开更多
Some aspects of anyon physics are reviewed with the intention of establishing a model for the quantization of the Hall conductance. A single particle Schrödinger model is introduced and coupled with a constra...Some aspects of anyon physics are reviewed with the intention of establishing a model for the quantization of the Hall conductance. A single particle Schrödinger model is introduced and coupled with a constraint equation formulated from the anyon picture. The Schrödinger equation-constraint system can be converted to a single nonlinear differential equation and solutions for the model can be produced.展开更多
文摘The note gives a watertight confirmation of the E-infinity Cantorian theory results for ordinary and dark cosmic energy density of the universe and respectively. The computation is fundamentally based on a golden mean fusion function that goes back to the highly original anyon proposal of F. Wilczek.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11804107)。
文摘Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore–Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore–Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.
基金the National Natural Science Foundation of China(Grant No.11465006),20200981-SIP-IPN,and the CONACyT(Grant No.288856-CB-2016).
文摘We show that it is possible to simulate an anyon by a trapped atom which possesses an induced electric dipole moment in the background of electric and magnetic fields in a specific configuration.The electric and magnetic fields we applied contain a magnetic and two electric fields.We find that when the atom is cooled down to the limit of the negligibly small kinetic energy,the atom behaves like an anyon because its angular momentum takes fractional values.The fractional part of the angular momentum is determined by both the magnetic and one of the electric fields.Roles electric and magnetic fields played are analyzed.
基金sponsored by the National Natural Science Foundation of China(Nos.12235007,11975131)。
文摘A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as super-symmetric quantum mechanics,super-symmetric gravity,super-symmetric string theory,super-symmetric integrable systems and so on.Supersymmetry and Grassmann numbers are,in some sense,dual conceptions,and it turns out that these conceptions coincide for the ren situation,that is,a similar conception of ren-number(R-number)is devised for ren-symmetry.In particular,some basic results of the R-number and ren-symmetry are exposed which allow one to derive,in principle,some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems.Training examples of ren-integrable KdV-type systems and ren-symmetric KdV equations are explicitly given.
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supported by the National Natural Science Foundation of China (Grant No. 11075099)
文摘We study quantum classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than h is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 27r-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.
基金Project supported by the National Natural Science Foundation of China(Grant No.11304062)
文摘We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, such as the Ising model,Hamiltonian model of quantum Hall effect, fermion pairing model, Kitaev honeycomb lattice model, and so on, are the short-range coupling cases of this knot lattice model. The long-range coupling knot lattice model bears Abelian and nonAbelian anyons, and shows integral and fractional filling states like the quantum Hall system. The fusion rules of anyons are explicitly demonstrated by braiding crossing states. The eigenstates of quantum models can be represented by a multilayer link lattice pattern whose topology is characterized by the linking number. This topological linking number offers a new quantity to explain and predict physical phenomena in conventional quantum models. For example, a convection flow loop is introduced into the well-known Bardeen–Cooper–Schrieffer fermion pairing model to form a vortex dimer state that offers an explanation of the pseudogap state of unconventional superconductors, and predicts a fractionally filled vortex dimer state. The integrally and fractionally quantized Hall conductance in the conventional quantum Hall system has an exact correspondence with the linking number in this multi-knot lattice model. The real-space knot pattern in the topological insulator model has an equivalent correspondence with the Lissajous knot in momentum space. The quantum phase transition between different quantum states of the quantum spin model is also directly quantified by the change of topological linking number, which revealed the topological character of phase transition. Circularized photons in an optical fiber network are a promising physical implementation of this multi-knot lattice, and provide a different path to topological quantum computation.
文摘The dynamics of neutral spinning particles in electromagnetic fields is investigated. The phase interference of unpolarized neutron beams is reasonably interpreted as the observed spin precession in external fields instead of potential effects in the quantum physics; namely, the Aharonov-Bohm and Aharonov-Casher effects. It is also pointed out that the recent experiment claimed to be the verification of Aharonov-Casher phase with neutron interferometry, however, can be considered as a test of new anyon model.
基金supported by the National Natural Science Foundation of China (Grant No. 11075099)
文摘We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.
基金Project supported in part by the National Natural Science Foundation of China.
文摘<正> By using the gauge-invariance,a Klein-Gordon’s type equation for anyons in external fields is constructed.The equation can be solved exactly in a constant electric and magnetic field,as well as in a quantized electromagnetic field.The analytic forms of solutions are also given in detail.
文摘Some aspects of anyon physics are reviewed with the intention of establishing a model for the quantization of the Hall conductance. A single particle Schrödinger model is introduced and coupled with a constraint equation formulated from the anyon picture. The Schrödinger equation-constraint system can be converted to a single nonlinear differential equation and solutions for the model can be produced.
