相关论文: On the Inozemtsev model

We introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability…

Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…

The present work shows that a properly chosen ordering of operators can restore unitarity in anisotropic quantum cosmological models. Bianch V and Bianchi IX models with a perfect fluid are worked out. It has been shown that a…

An infinite-dimensional version of Calogero-Moser operator of $BC$-type and the corresponding Jacobi symmetric functions are introduced and studied, including the analogues of Pieri formula and Okounkov's binomial formula. We use this to…

The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…

Continuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric…

A hyperbolic BC(n) Sutherland model involving three independent coupling constants that characterize the interactions of two types of particles moving on the half-line is derived by Hamiltonian reduction of the free geodesic motion on the…

We investigate the classical Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the sympletic Weyl-Moyal formalism we find that noncommutativity induces a non-vanishing…

Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…

We investigate the transport behavior of finite modular quantum systems. Such systems have recently been analyzed by different methods. These approaches indicate diffusive behavior even and especially for finite systems. Inspired by these…

We study the interplay of symmetries and Gaussianity in bosonic systems, under closed and open dynamics, and develop a resource theory of Gaussian asymmetry. Specifically, we focus on Gaussian symmetry-respecting (covariant) operations,…

The Nelson model describes the interaction of nonrelativistic quantum particles with a relativistic quantum field of scalar bosons. Nelson rigorously demonstrated in 1964 the existence of a well-defined self-adjoint Nelson Hamiltonian by…

The vacuum expectation value of the evolution operator for a general class of Hamiltonians used in quantum field theory and statistical physics and which include unstable particles is considered. An exact formula which describes the large…

Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…

The BBM equation is a Hamiltonian PDE which revealed to be a very interesting test-model to study the transformation property of Gaussian measures along the flow. In this paper we study the BBM equation with critical dispersion (which is a…

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…

We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite…

We study the movement of the living organism in a band form towards the presence of chemical substrates based on a system of partial differential evolution equations. We incorporate Einstein's method of Brownian motion to deduce the…

The Bayesian approach to ill-posed operator equations in Hilbert space recently gained attraction. In this context, and when the prior distribution is Gaussian, then two operators play a significant role, the one which governs the operator…