相关论文: Isoperiodic classical systems and their quantum co…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess…
The key to optical analogy to a multi-particle quantum system is the scalable property. Optical elds modulated with pseudorandom phase sequences is an interesting solution. By utilizing the properties of pseudorandom sequences, mixing…
It is known that the algebraic \deRham cohomology group $\hDR{i}(X_0/\Q)$ of a nonsingular variety $X_0/\Q$ has the same rank as the rational singular cohomology group $\h^i\sing(\Xh;\Q)$ of the complex manifold $\Xh$ associated to the base…
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful…
In this paper for the first time, we construct quantum analogs starting from classical stochastic processes, by replacing random which path decisions with superpositions of all paths. This procedure typically leads to non-unitary quantum…
This paper is a brief review of classical and quantum transport phenomena, as well as related spectral properties, exhibited by one-dimensional periodically kicked systems. Two representative and fundamentally different classes of systems…
Adiabatic evolution is an emergent design principle for time modulated metamaterials, often inspired by insights from topological quantum computing such as braiding operations. However, the pursuit of classical adiabatic metamaterials is…
We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast to the standard nonperiodic case where either…
Macroscopic ensembles of radiating dipoles are ubiquitous in the physical and natural sciences. In the classical limit the dipoles can be described as damped-driven oscillators, which are able to spontaneously synchronize and collectively…
Li\'{e}nard-type nonlinear oscillators with linear and nonlinear damping terms exhibit diverse dynamical behavior in both the classical and quantum regimes. In this paper, we consider examples of various one-dimensional Li\'{e}nard type-I…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional…
We consider the rational potentials of the one-dimensional mechanical systems, which have a family of periodic solutions with the same period (isochronous potentials). We prove that up to a shift and adding a constant all such potentials…
While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the…
The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which…