相关论文: Continuous canonical transformation for the double…
This pedagogical work presents the significant role that canonical transformation plays in the interpretation of the Abelian bosonized single-channel SU(2) Kondo model, emphasizing its effect on the scaling dimension $\Delta$. The…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm…
Paper is devoted to maintaining the simple objective: We want to provide Hamiltonian canonical form for autonomous dynamical system reducible to even-dimensional one. Along the road we construct new class of conserved quantities, called…
In classical mechanics, we can describe the dynamics of a given system using either the Lagrangian formalism or the Hamiltonian formalism, the choice of either one being determined by whether one wants to deal with a second degree…
This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet,…
A high-order extension is presented for the electromagnetic gyrokinetic formulation in which the parallel canonical momentum is taken as one of phase space coordinates. The high-order displacement vector associated with the guiding-center…
The offset linear canonical transform encompassing the numerous integral transforms, is a promising tool for analyzing non-stationary signals with more degrees of freedom. In this paper, we generalize the windowed offset linear canonical…
Following Dirac, the rules of canonical quantization include classical and quantum contact transformations of classical and quantum phase space variables. While arbitrary classical canonical coordinate transformations exist that is not the…
A {\em complex} canonical transformation is found that takes the fourth order derivative Pais-Uhlenbeck oscillator into two independent harmonic oscillators thus showing that this model has energy bounded from below, unitary time-evolution…
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…
Dynamical canonical systems and their connections with the classical (spectral) canonical systems are considered. We construct B\"acklund-Darboux transformation and explicit solutions of the dynamical canonical systems. We study also those…
We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the…
We develop a canonical form for congruence of max plus symmetric matrices. We use the same canonical form to get results in the generalized eigenvector problem. We have also utilized the canonical form to find all symmetric matrices that…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
We put forth a new class of quantum master equations that correctly reproduce the asymptotic state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of…
The Hamilton-Jacobi formalism for fermionic systems is studied. We derive the HJ equations from the canonical transformation procedure, taking into account the second class constraints typical of these systems. It is shown that these…