相关论文: Quasiclassical Asymptotics and Coherent States for…

Results of investigation of the asymptotic behavior of solutions to the Cauchy problems for a quasi-linear parabolic equation with a small parameter at a higher derivative near singular points of limit solutions are presented. Interest to…

In this paper we discuss a new approach to the quasinormal-mode problem in general relativity. By combining a characteristic formulation of the perturbation equations with the integration of a suitable phase-function for a complex valued…

There are few exactly solvable potentials in quantum mechanics for which the completeness relation of the energy eigenstates can be explicitly verified. In this article, we give an elementary proof that the set of bound (discrete) states…

In this paper we present a generic form of the cosmological Equation of State derived from the formalism of Statistical Mechanics, assuming that a cosmic acceleration scenario can be interpreted as a system of quasi-particles. By…

In this article, we study the asymptotic fields of the Yukawa particle-field model of quantum physics, in the semiclassical regime $\hslash\to 0$, with an interaction subject to an ultraviolet cutoff. We show that the transition amplitudes…

Quantum technology is increasingly relying on specialised statistical inference methods for analysing quantum measurement data. This motivates the development of "quantum statistics", a field that is shaping up at the overlap of quantum…

A survey on the dynamical and thermodynamical properties of plasmas with strong Coulomb interactions in the quasi-classical density-temperature region is given. First the basic theoretical concepts describing nonideality are discussed. The…

We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for…

The dynamics of an ensemble of $N$ weakly coupled limit-cycle oscillators can be captured by their $N$ phases using standard phase reduction techniques. However, it is a phenomenological fact that all-to-all strongly coupled limit-cycle…

We derive general properties, which hold for both quantum and classical systems, of response functions of nonequilibrium steady states. We clarify differences from those of equilibrium states. In particular, sum rules and asymptotic…

This paper aims to stress the role of the Cahill-Glauber quasi-probability densities in defining, detecting, and quantifying the non-classicality of field states in quantum optics. The distance between a given pure state and the set of all…

For spectral actions consisting of the average number of particles and arising from open systems made of general free $q$-particles (including Bose, Fermi and classical ones corresponding to $q=\pm 1$ and $0$, respectively) in thermal…

We derive a semi-classical formula for computing the spectrum of bound states made of Majorana fermions in a generic non-integrable 2d quantum field theory with a set of degenerate vacua. We illustrate the application of the formula in a…

We consider the spectrum of BPS saturated states in $N = 2$ gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which…

We use exact symmetry properties of the two-dimensional quantum compass model to derive nonequivalent invariant subspaces in the energy spectra of $L\times L$ clusters up to L=6. The symmetry allows one to reduce the original $L\times L$…

We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…

We consider the semi-classical limit of the quantum evolution of Gaussian coherent states whenever the Hamiltonian $\mathsf H$ is given, as sum of quadratic forms, by $\mathsf H=…

We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of…

The semiclassical limit of a 4-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a non-degenerate 4-simplex geometry, the asymptotic formula contains the Regge…

In this paper we study the existence of bound states of the following class of quasilinear problems, \begin{equation*} \left\{ \begin{aligned} &-\varepsilon ^p\Delta_pu+V(x)u^{p-1}=f(u)+u^{p^\ast -1},\ u>0,\ \text{in}\ \mathbb{R}^{N}, &\lim…