相关论文: Representations of Generalized a$_r$ Statistics an…
The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
We develop an analytical approach to quantum Gaussian states in infinite-mode representation of the Canonical Commutation Relations (CCR's), using Yosida approximations to define integrability of possibly unbounded observables with respect…
While dealing with a class of generalized Bargmann spaces, we rederive their reproducing kernels from the knowledge of an orthonormal basis by using an addition formula for Laguerre polynomials involving the disk polynomials. We construct…
For continuous-time dynamical systems with reversible trajectories, the nowhere-vanishing eigenfunctions of the Koopman operator of the system form a multiplicative group. Here, we exploit this property to accelerate the systematic…
It has been shown that a positive semi-definite Hamiltonian H, that has a tridiagonal matrix representation in a given basis, can be represented in the form H = A{\dag}A, where A is a forward shift operator playing the role of an…
In the language of random counting measures many structural properties of the Poisson process can be studied in arbitrary measurable spaces. We provide a similarly general treatise of Gibbs processes. With the GNZ equations as a definition…
We present a general framework for the efficient simulation of realistic fermionic systems with modern machine learning inspired representations of quantum many-body states, towards a universal tool for ab initio electronic structure. These…
We review how the identification of gauge theory operators representing string states in the pp-wave/BMN correspondence and their associated anomalous dimension reduces to the determination of the eigenvectors and the eigenvalues of a…
Consider the family of power divergence statistics based on $n$ trials, each leading to one of $r$ possible outcomes. This includes the log-likelihood ratio and Pearson's statistic as important special cases. It is known that in certain…
Characteristic uncertainty relations and their related squeezed states are briefly reviewed and compared in accordance with the generalizations of three equivalent definitions of the canonical coherent states. The standard SU(1,1) coherent…
Collective operators that describe interaction of generic quantum system with discrete spectrum with a quantum field are investigated. These operators, considered as operators in the entangled Fock space (space generated by action of…
We present an approach to generalised fermionic statistics which relates the existence of a generalised statistical behaviour to non-invariant ground states. Considering the thermal average of an operatorial generalization of the Heisenberg…
By a Wigner-function calculation, we evaluate the trace of a certain Gaussian operator arising in the theory of a boson system subject to both finite temperature and (weak) interaction. Thereby we rederive (and generalize) a recent result…
In this paper we make a clear relationship between the automorphic representations and the quantization through the Geometric Langlands Correspondence. We observe that the discrete series representation are realized in the sum of…
We consider Gaussian states of fermionic systems and study the action of the partial transposition on the density matrix. It is shown that, with a suitable choice of basis, these states are transformed into a linear combination of two…
A dynamical algebra ${\cal A}_q$, englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the…
We study regularity of bound states pertaining to embedded eigenvalues of a self-adjoint operator $H$, with respect to an auxiliary operator $A$ that is conjugate to $H$ in the sense of Mourre. We work within the framework of singular…
The Hamiltonian reggeon acting in Bargmann space is non-Hermitian with respect to the standard scalar product associated to Bargmann space. Hence the question arises, whether the eigenfunctions by the finite norm condition form a complete…
Based on the generalized Boltzmann equation and the reverse function of the distribution function, we investigate the two-parameter generalized statistics and get an expression between the two parameters (k,r) and the physical quantities…