Related papers: On the Coherent State Path Integral for Linear Sys…
We derive the first order canonical formulation of cosmological perturbation theory in a Universe filled by a few scalar fields. This theory is quantized via well-defined Hamiltonian path integral. The propagator which describes the…
By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the…
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in…
We study the application of the coherent-state path integral as a numerical tool for wave-packet propagation. The numerical evaluation of path integrals is reduced to a matrix-vector multiplication scheme. Together with a split-operator…
The path-integral of the fermionic oscillator with a time-dependent frequency is analyzed. We give the exact relation between the boundary condition to define the domain in which the path-integral is performed and the transition amplitude…
In this paper we introduce a method for finding a time independent Hamiltonian of a given dynamical system by canonoid transformation. We also find a condition that the system should satisfy to have an equivalent time independent…
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially…
In this work, we have applied the integrals of motion method in a nonunitary approach and so obtained the time-dependent displacement and squeezed parameters of the coherent squeezed states (CSS). On its turn, CSS for one-dimensional…
Given any covariance matrix corresponding to a so-called pure Gaussian state, a linear quantum system can be designed to achieve the assigned covariance matrix. In most cases, however, one might obtain a system that is difficult to realize…
Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary…
We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
The paper first discusses theoretically the off-resonance selective excitation method that is dependent on the atomic internal states and used to generate approximately a standard coherent state of harmonic oscillator. The coherent average…
We construct integrable models on flag manifold by using the symplectic structure explicitly given in the Bruhat coordinatization of flag manifold. They are non-commutative integrable and some of the conserved quantities are given by the…
The propagator for a certain class of two time-dependent coupled and driven harmonic oscillators with time-varying angular frequencies and masses is evaluated by path integration. This is simply done through suitably chosen generalized…
The most general form of Hamiltonian that preserves fermionic coherent states stable in time is found in the form of nonstationary fermion oscillator. Invariant creation and annihilation operators and related Fock states and coherent states…
Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a "sourrounded" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on…