Related papers: A semiclassical trace formula for the canonical pa…
A general formula for the canonical partition function for a system obeying any statistics based on the permutation group is derived. The formula expresses the canonical partition function in terms of sums of Schur functions. The only…
The progress in two-dimensional materials has led to rapid experimental developments in quantum plasmonics, where light is manipulated using plasmons. Although numerical methods can be used to quantitatively describe plasmons in spatially…
We present a semiclassical analysis for a dissipative quantum map with an area-nonpreserving classical limit. We show that in the limit of Planck's constant to 0 the trace of an arbitrary natural power of the propagator is dominated by…
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of…
We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of…
Although partition temperature derived using the Darwin-Fowler method is exact for simple scenarios, the derivation for complex systems might reside on specific approximations whose viability is not ensured if the thermodynamic limit is not…
This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…
We consider a quantum system of non-interacting fermions at temperature T, in the framework of linear response theory. We show that semiclassical theory is an appropriate framework to describe some of their thermodynamic properties, in…
We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a $2\times 2$ symmetric matrix. Previous results on this problem were restricted either to the case where the…
We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self--interacting fermionic models to show, in one-space dimension, a general relation among the…
For relativistic particles with spin 1/2, which are described by the Dirac equation, a semiclassical trace formula is introduced that incorporates expectation values of observables in eigenstates of the Dirac-Hamiltonian. Furthermore, the…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar…
We provide a semiclassical description of the double-slit experiment based on momentous quantum mechanics, where the implementation of canonical variables facilitate the derivation of the equations of motion for the system. We show the…
We consider composite quantum-dynamical systems that can be partitioned into weakly interacting subsystems, similar to system-bath type situations. Using a factorized wave function ansatz, we mathematically characterize dynamical scale…
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees…
We present a novel semiclassical framework tailored to determine the scaling dimensions of heavy neutral composite operators in conformal field theories (CFTs) which are inaccessible with other current methodologies. It utilizes the…
The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary…