scholarly journals Size-effect at finite temperature in a quark–antiquark effective model in phase space

2021 ◽  
pp. 2150121
Author(s):  
G. X. A. Petronilo ◽  
R. G. G. Amorim ◽  
S. C. Ulhoa ◽  
A. F. Santos ◽  
A. E. Santana ◽  
...  
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Size Effect ◽  
Wigner Function ◽  
Ground State ◽  
Finite Temperature ◽  
Size Effects ◽  
Schrodinger Equation ◽  
Effective Model ◽  
Linear Potential

A quark–antiquark effective model is studied in a toroidal topology at finite temperature. The model is described by a Schrödinger equation with linear potential which is embedded in a torus. The following aspects are analyzed: (i) the nonclassicality structure using the Wigner function formalism; (ii) finite temperature and size-effects are studied by a generalization of Thermofield Dynamics written in phase space; (iii) in order to include the spin of the quark, Pauli-like Schrödinger equation is used; (iv) analysis of the size-effect is considered to observe the fluctuation in the ground state. The size effect goes to zero at zero, finite and high temperatures. The results emphasize that the spin is a central aspect for this quark–antiquark effective model.

scholarly journals Quantum Physics in Phase Space: an Analysis of Simple Pendulum

2018 ◽  
Vol 1 (2) ◽  
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Schrödinger Equation ◽  
Wigner Function ◽  
Schrodinger Equation ◽  
Quantum Physics ◽  
Symplectic Structure ◽  
Unitary Representations ◽  
Galilei Group ◽  
Simple Pendulum

In this work we present a brief review about quantum mechanics in phase space. The approach discussed is based in the notion of symplectic structure and star-operators. In this sense, unitary representations for the Galilei group are construct, and the Schrodinger equation in phase space is derived. The connection between phase space amplitudes and Wigner function is presented. As a new result we solved the Schrodinger equation in phase space for simple pendulum. PACS Numbers: 11.10.Nx, 11.30.Cp, 05.20.Dd

On the mapping connecting the cylindrical nonlinear von Neumann equation with the standard von Neumann equation

2010 ◽  
Vol 76 (3-4) ◽  
pp. 645-653 ◽  
Author(s):  
RENATO FEDELE ◽  
SERGIO DE NICOLA ◽  
DUSAN JOVANOVIĆ ◽  
DAN GRECU ◽  
ANCA VISINESCU
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Wigner Function ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Von Neumann ◽  
Nonlinear Schrödinger ◽  
Von Neumann Equation

AbstractThe Wigner transformation is used to define the quasidistribution (Wigner function) associated with the wave function of the cylindrical nonlinear Schrödinger equation (CNLSE) in a way similar to that of the standard nonlinear Schrödinger equation (NLSE). The phase-space equation, governing the evolution of such quasidistribution, is a sort of nonlinear von Neumann equation (NLvNE), called here the ‘cylindrical nonlinear von Neumann equation’ (CNLvNE). Furthermore, the phase-space transformations, connecting the Wigner function and the NLvNE with the ‘cylindrical Wigner function’ and the CNLvNE, are found by extending the configuration space transformations that connect the NLSE and the CNLSE. Some examples of phase-space soliton solutions are given analytically and evaluated numerically.

Analytical solution for quantum quartic oscillator in phase space

2020 ◽  
Vol 35 (20) ◽  
pp. 2050100
Author(s):  
A. X. Martins ◽  
T. M. R. Filho ◽  
R. G. G. Amorim ◽  
R. A. S. Paiva ◽  
G. Petronilo ◽  
...  
Keyword(s):  
Phase Space ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Wigner Function ◽  
Schrodinger Equation ◽  
Unitary Representations ◽  
Algebraic Methods ◽  
Quantum Oscillator ◽  
Galilei Group ◽  
Lie Methods

In this work, we address the quartic quantum oscillator in phase space using two approaches: computational and algebraic methods. In order to achieve such an aim, we built simplistic unitary representations for Galilei group, as a consequence the Schrödinger equation is derived in the phase space. In this context, the amplitudes of quasi-probability are associated with the Wigner function. In a computational way, we apply the techniques of Lie methods. As a result, we determine the solution of the quantum oscillator in the phase space and calculate the corresponding Wigner function. We also calculated the negativity parameter of the analyzed system.

Existence of a Ground State Solution for a Quasilinear Schrödinger Equation

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Xiang-dong Fang ◽  
Zhi-qing Han
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
State Solution ◽  
Quasilinear Schrödinger Equation

AbstractIn this paper we are concerned with the quasilinear Schrödinger equation−Δu + V(x)u − Δ(uwhere N ≥ 3, 4 < p < 4N/(N − 2), and V(x) and q(x) go to some positive limits V

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