English
Related papers

Related papers: Analytical Solution for Gross-Pitaevskii Equation …

200 papers

We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that can not be expressed as a convex mixture of Gaussian states. In particular we prove that, for convex mixtures of…

We consider the nonlinear Schr{\"o}dinger equation with a potential, also known as Gross-Pitaevskii equation. By introducing a suitable spectral localization, we prove low regularity error estimates for the time discretization corresponding…

Analysis of PDEs · Mathematics 2025-07-22 Rémi Carles

We present the reconstruction of the Wigner function of a classical phase-sensitive state, a pulsed coherent state, by measurements of the distributions of detected-photons of the state displaced by a coherent probe field. By using a hybrid…

Quantum Physics · Physics 2016-04-27 Maria Bondani , Alessia Allevi , Alessandra Andreoni

We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner…

Mathematical Physics · Physics 2014-11-20 C. Bastos , N. C. Dias , J. N. Prata

The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…

Quantum Physics · Physics 2019-02-01 E M Graefe , B Longstaff , T Plastow , R Schubert

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B 35,1555,(2002). The derivation does not rely on the concept of local energy and momentum…

Condensed Matter · Physics 2010-11-02 C. W. Gardiner , M. J. Davis

We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a non-linear Schroedinger equation used to simulate the dynamics of Bose-Einstein condensates. Considering condensates trapped in harmonic potentials, we…

Soft Condensed Matter · Physics 2007-05-23 Claude M. Dion , Eric Cances

We consider the cubic nonlinear Schrodinger equation with a potential in one space dimension. Under the assumptions that the potential is generic, sufficiently localized, and does not have bound states, we obtain the long time asymptotic…

Analysis of PDEs · Mathematics 2017-04-04 Pierre Germain , Fabio Pusateri , Frederic Rousset

We show that the Schr\"{o}dinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extended Weyl calculus obtained by letting the Heisenberg group act on…

Symplectic Geometry · Mathematics 2009-11-11 Maurice De Gosson

We discuss an ab initio world-line approach to constructing phase space distributions in systems with internal symmetries. Starting from the Schwinger-Keldysh real time path integral in quantum field theory, we derive the most general…

High Energy Physics - Theory · Physics 2019-03-13 Niklas Mueller , Raju Venugopalan

A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any…

Chaotic Dynamics · Physics 2007-12-12 Holger Waalkens , Roman Schubert , Stephen Wiggins

The effects of interpreting classical phase space distributions as Wigner functions, which is common in models of multiparticle production, are discussed. The temperature for the classical description is always higher than that for its…

High Energy Physics - Phenomenology · Physics 2009-04-22 K. Zalewski

We formulate, with full generality, the asymptotic estimation theory for Gaussian states in terms of their first and second moments. By expressing the quantum Fisher information (QFI) and the elusive symmetric logarithmic derivative (SLD)…

Quantum Physics · Physics 2013-03-18 Alex Monras

While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge…

Mathematical Physics · Physics 2017-04-19 S. Hasibul Hassan Chowdhury , Hishamuddin Zainuddin

We show that Wigner-Leggett-Caldeira equation for Wigner phase space distribution function which describes the quantum Brownian motion of a particle in a force field in a high temerature, Ohmic environment can be identified as a…

Statistical Mechanics · Physics 2009-10-31 Jyotipratim Ray Chaudhuri , Bidhan Chandra Bag , Deb Shankar Ray

It is proved that approximations which are obtained as solutions of the multiphase Whitham modulation equations stay close to solutions of the original equation on a natural time scale. The class of nonlinear wave equations chosen for the…

Analysis of PDEs · Mathematics 2020-11-11 Tom Bridges , Anna Kostianko , Guido Schneider

Wigner functions are broadly used to probe non-classical effects in the macroscopic world. Here we develop an orbital-free functional framework to compute the 1-body Wigner quasi-probability for both fermionic and bosonic systems. Since the…

Strongly Correlated Electrons · Physics 2024-01-18 Carlos L. Benavides-Riveros

A quasi-particle theory for monatomic gases in equilibrium is formulated and evaluated to yield the exact virial contributions to the thermodynamic state functions in lowest order of the density. Van der Waals blocking has necessarily to be…

Statistical Mechanics · Physics 2007-05-23 K. Baerwinkel , J. Schnack , U. Thelker

We have found an effective method of calculating the Wigner function, being a quantum analogue of joint probability distribution of position and momentum, for bound states of nonrelativistic hydrogen atom. The formal similarity between the…

Quantum Physics · Physics 2009-11-11 L. Praxmeyer , J. Mostowski , K. Wodkiewicz

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…

Quantum Physics · Physics 2009-11-11 Arthur O. Pittenger , Morton H. Rubin