On the transition from ferromagnetism to antiferromagnetism on twofold Cayley tree

Summary A fixed-point conversion theorem which shows the transition from ferromagnetism to antiferromagnetism on twofold Cayley tree is proved. The ferromagnetic and antiferromagnetic maps are shown to be related by an involution and in zero field the stable fixed points of the ferromagnetic map are converted to a stable two-cycle of the antiferromagnetic map. A reduced one-dimensional analysis in zero field yields precisely the same results.     

Chiral crossover characterized by Mott transition at finite temperature

We discuss the proper definition for the chiral crossover at finite temperature,based on Goldstone's theorem.Different from the commonly used maximum change in chiral condensate,we propose defining the crossover temperature using the Mott transition of pseudo-Goldstone bosons,which,by definition,guarantees Goldstone's theorem.We analytically and numerically demonstrate this property in the frame of a Pauli-Villars regularized NJL model.In an external magnetic field,we find that the Mott transition temperature shows an inverse magnetic catalysis effect.     

留数定理在拓扑相变中的应用

留数定理是高校物理专业必修课程数学物理方法中的一个重要定理.传统教学中关于该定理的讲授着重于数学公式的推导和数学思想的传达,而对于其在具体物理问题上的应用鲜有涉及.本文以一维Su-Schrieffer-Heeger模型的拓扑相变问题为例,阐明了如何利用留数定理解析得到二阶位移量的表达式并用该物理量表征拓扑相变.在讲授留数定理的教学过程中引入具体物理问题的分析实例,可以使学生更深刻地理解数学定理中的物理内涵.     

Computing the Topological Entropy for Piecewise Monotonic Maps on the Interval

A new method for computing the topological entropy of a piecewise monotonic transformation on the interval is presented. It uses a transition matrix associated with the transformation. For this matrix we give a spectral theorem. This can be used for an estimation of the accuracy of the algorithm.     

Isoscalar transition rates and an implicit double folding model using density-dependent forces

A generalization of the Satchler theorem, regarding the radial moments of single folded potentials to the case of a double-folding model is obtained. A proper accounting of the density-dependence of the nucleon-nucleon force is shown to remove the long standing disparity between the isoscalar transition rates deduced from alpha inelastic scattering to those obtained from electromagnetic transitions. The strong l dependence of the disparity is accounted for.     

The Fluctuation Theorem as a Gibbs Property

Common ground to recent studies exploiting relations between dynamical systems and nonequilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity principle) underlying the Gallavotti–Cohen fluctuation theorem make it possible, using symbolic dynamics, to employ the theory of one-dimensional lattice spin systems. The Kurchan and Lebowitz–Spohn analysis of this fluctuation theorem for stochastic dynamics can be restated on the level of the space-time measure which is a Gibbs measure for an interaction determined by the transition probabilities. In this note we understand the fluctuation theorem as a Gibbs property, as it follows from the very definition of Gibbs state. We give a local version of the fluctuation theorem in the Gibbsian context and we derive from this a version also for some class of spatially extended stochastic dynamics.     

Gas-liquid phase transition

A theorem has been proved giving a sufficient condition for a first order phase transition in a gas. The corresponding fugacity expansions for the isotherms in the different phases have been derived. A synopsis of this paper was presented at the International Conference on Statistical Physics at Budapest, 1975. This paper is the revised version of an earlier paper published by the author (Biswas 1973) and subsequently criticized by Groeneveld (Groeneveld 1973). This paper is self-complete and free from the objections raised by Groeneveld about the earlier paper.     

A Possible Operational Motivation for the Orthocomplementation in Quantum Structures

In the foundations of quantum mechanics Gleason’s theorem dictates the uniqueness of the state transition probability via the inner product of the corresponding state vectors in Hilbert space, independent of which measurement context induces this transition. We argue that the state transition probability should not be regarded as a secondary concept which can be derived from the structure on the set of states and properties, but instead should be regarded as a primitive concept for which measurement context is crucial. Accordingly, we adopt an operational approach to quantum mechanics in which a physical entity is defined by the structure of its set of states, set of properties and the possible (measurement) contexts which can be applied to this entity. We put forward some elementary definitions to derive an operational theory from this State–COntext–Property (SCOP) formalism. We show that if the SCOP satisfies a Gleason-like condition, namely that the state transition probability is independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented, which is one of the ‘quantum axioms’ used in the Piron–Solèr representation theorem for quantum systems. In this sense we obtain a possible physical meaning for the orthocomplementation widely used in quantum structures.     

On the transition temperature of ferroelectric and the Blume-Hubbard scheme

A way to derive upper and lower bounds for the transition temperature of a general system is introduced and applied to the transverse Ising model using the Blume-Hubbard decoupling scheme but without invoking the fluctuation-dissipation theorem.     

受激渡越辐射光学速调管

本文提出一种基于受激渡越辐射的的光学速调管新方案。应用著名的Madey定理对这种新型的自由电子激光器进行了分析和计算,其中包括自发辐射的和受激辐射的分析讨论。结果表明,Madey定理确能简化复杂的计算,并给出清楚的物理概念;同时计算还表明,受激渡越辐射光学速调管具有大的输出增益。文中对N个介质区构成的多级光学速调管情形也进行了讨论。 关键词：     

Quantum Probability’s Algebraic Origin

Max Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further physically meaningful and experimentally verifiable novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg’s and others’ uncertainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.     

Fluctuation symmetry in a two-state Markov model

We show that the scaled cumulant generating and large deviation function, associated to a two-state Markov process involving two processes, obey a symmetry relation reminiscent of the fluctuation theorem, independent from any conditions on the transition rates. The Legendre transform leading from the scaled cumulant generating function to the large deviation function is performed in an ingenious way, avoiding the sign problem associated to taking a square root. Applications to the theory of random walks and to the stochastic thermodynamics for a quantum dot are presented.     

Pseudo analytical solution to time periodic stiffness systems

An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudoclosed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed,based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.     

Landau problem with a general time-dependent electric field

The time evolution is studied for the Landau level problem with a general time dependent electric field E(t) in a plane perpendicular to the magnetic field. A general and explicit factorization of the time evolution operator is obtained with each factor having a clear physical interpretation. The factorization consists of a geometric factor (path-ordered magnetic translation), a dynamical factor generated by the usual time-independent Landau Hamiltonian, and a nonadiabatic factor that determines the transition probabilities among the Landau levels. Since the path-ordered magnetic translation and the nonadiabatic factor are, up to completely determined numerical phase factors, just ordinary exponentials whose exponents are explicitly expressible in terms of the canonical variables, all of the factors in the factorization are explicitly constructed. New quantum interference effects are implied by this result. The factorization is unique from the point of view of the quantum adiabatic theorem and provides a seemingly first rigorous demonstration of how the quantum adiabatic theorem (incorporating the Berry phase phenomenon) is realized when infinitely degenerate energy levels are involved. Since the factorization separates the effect caused by the electric field into a geometric factor and a nonadiabatic factor, it makes possible to calculate the nonadiabatic transition probabilities near the adiabatic limit. A formula for matrix elements that determines the mixing of the Landau levels for a general, nonadiabatic evolution is also provided by the factorization.     

Critical point behavior of the Wilson loop

I note that, at a second-order phase transition in a gauge theory, the static quark-antiquark potential derived from the Wilson loop is proportional to $\text{1}\text{R}$, independently of space-time dimensionality. I present two simple applications of this observation: a definition of the critical exponent η for lattice gauge theories and an argument for gauge theories analogous to the Mermin-Wagner theorem.     

No-pumping theorem for non-Arrhenius rates

The no-pumping theorem refers to a Markov system that holds the detailed balance, but is subject to a time-periodic external field. It states that the time-averaged probability currents nullify in the steady periodic (Floquet) state, provided that the Markov system holds the Arrhenius transition rates. This makes an analogy between features of steady periodic and equilibrium states, because in the latter situation all probability currents vanish explicitly. However, the assumption on the Arrhenius rates is fairly specific, and it need not be met in applications. Here a new mechanism is identified for the no-pumping theorem, which holds for symmetric time-periodic external fields and the so called destination rates. These rates are the ones that lead to the locally equilibrium form of the master equation, where dissipative effects are proportional to the difference between the actual probability and the equilibrium (Gibbsian) one. The mechanism also leads to an approximate no-pumping theorem for the Fokker-Planck rates that relate to the discrete-space Fokker-Planck equation.     

An RPA model for the description of one-nucleon emission processes and application to 16O(γ, N) reactions

A coordinate space RPA formalism is proposed to handle one-nucleon emission processes in a self-consistent way. A method is outlined to solve the RPA equations so obtained for the whole class of rotationally invariant effective interactions, including those having a velocity dependence. The method is used to study ¹⁶O(γ, N) reactions with Skyrme-type effective interactions. The use of the long-wavelength approximation (LWA) when handling reactions of this type at medium energies, is criticized. Different alternative forms for the electric transition operators are used, applying Siegert's theorem or not, and it is shown that at higher momentum transfer, the obtained results are strongly sensitive to it. We emphasize that especially beyond energy regions where the LWA is valid, the use of Siegert's theorem should be carefully examined.     

A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux-quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum space construction of the zero-mode solution presented here is complementary to the approximate real space solution of the Bogoliubov-de Gennes equations at a vortex core (Sau et al., arXiv:0907.2239 [17]), proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.     

Linear response domain in glassy systems

Molecular dynamics simulations are performed on a realistic glass forming model system. The linear and nonlinear response domains are explored numerically for the case where one of the particles interacts with a constant external force. As the temperature is lowered towards the glass transition, we find that the range of fields over which the response is linear shrinks towards zero. We show that the time required for convergence of the steady state fluctuation theorem and the valid application of the central limit theorem becomes very large as the glass transition is approached. This in turn implies that the domain over which a linear response can be observed becomes progressively smaller.