Related papers: Functional Wigner representation of BEC quantum dy…
Phase-space methods allow one to go beyond the mean-field approximation to simulate the quantum dynamics of interacting fields. Here, we obtain a technique for initializing either Wigner or positive-P phase-space simulations of…
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary…
We calculate the atomic (spin) Wigner function for the single mode Dicke model in the regime of large number of two-level atoms. The dynamics of this quasi-probability function on the Bloch sphere allows us to visualize the consequences of…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
A full treatment of decoherence and dephasing effects in BEC interferometry has been developed based on using quantum correlation functions for treating interferometric effects. The BEC is described via a phase space distribution functional…
We develop a discrete truncated Wigner method to analyze the real-time evolution of dissipative SU(${\cal N}$) spin systems coupled with a Markovian environment. This semiclassical approach is not only numerically efficient but also…
Non-Gaussian correlations in a pure state are inextricably linked with non-classical features, such as a non positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the…
Weakly nonlinear energy transfer between normal modes of strongly resonant PDEs is captured by the corresponding effective resonant systems. In a previous article, we have constructed a large class of such resonant systems (with specific…
Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being…
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
In quantum mechanics, the Wigner function $\rho_W(\textbf{r},\textbf{p})$ serves as a phase-space representation, capturing information about both the position $\textbf{r}$ and momentum $\textbf{p}$ of a quantum system. The Wigner function…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…
The truncated Wigner and positive-P phase-space representations are used to study the dynamics of a one-dimensional Bose gas. This allows calculations of the breathing quantum dynamics of higher-order solitons with 10^{3}-10^{5} particles,…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…
We demonstrate a method which allows the stochastic modelling of quantum systems for which the generalised Fokker-Planck equation in the phase space contains derivatives of higher than second order. This generalises quantum stochastics far…
Variational method is applied to describe Bose-Einstein condensates (BEC) interacting via a pseudo-potential, taking into account quantum fluctuations around the mean field by the Gaussian approximation. Contributions from the pair-wise…
Bubble-shaped Bose-Einstein condensates (BECs) constitute a unique class of quantum fluids with a hollow, thin-shell geometry that supports a wide variety of phenomena that are distinct from those of compact condensates. Numerical…
The computation of the ground states of spin-$F$ Bose-Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize the energy functional and constraints using the Fourier…