Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1209.5952 · Physical Review B

Quantum collapses and revivals of matter wave in dynamics of symmetry breaking

Frank Kirtschig, Jorrit Rijnbeek, Jeroen van den Brink, Carmine Ortix

Published Jan 25, 2013• 0 citations
arXivHTMLPDF

Abstract

Quantum processes can be described in terms of a quasiprobability distribution (the Wigner distribution) analogous to the phase-space probability distribution of the classical realm. In contrast to the incomplete glimpse of the wave function that is achievable in a single shot experiment, the Wigner distribution, accessible by quantum state tomography, reflects the full quantum state. We show that during the fundamental symmetry-breaking process of a generic quantum system, with a symmetry-breaking field driving the quantum system far from equilibrium, the Wigner distribution evolves continuously with the system undergoing a sequence of revivals into the symmetry-unbroken state, followed by collapses onto a quasiclassical state akin to the one realized in infinite-size systems. We show that generically this state is completely delocalized both in momentum and in real space.

DOI
10.1103/physrevb.87.014304

Related papers

Wigner quasi-probability distribution for the infinite square well: energy eigenstates and time-dependent wave packets

Belloni, M, Doncheski, M A, Robinett, R W

We calculate the Wigner quasi-probability distribution for position and momentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite well potential, using both x- and p-space stationary-state solutions, as well as visualizing the results. We then evaluate the time-dependent Wigner distribution, P_W(x,p;t), for Gaussian wave packet solutions of this system, illustrating both the short-term semi-classical time dependence, as well as longer-term revival and fractional revival behavior and the structure during the collapsed state. This tool provides an excellent way of demonstrating the patterns of highly correlated Schrodinger-cat-like `mini-packets' which appear at fractional multiples of the exact revival time.

•Dec 9, 2003•28 citations

Connection between Wigner distribution of nonclassical fields and collapse-revival of atomic dynamics

C. H. Raymond Ooi

The transient evolution of nonclassical radiation fields interacting with an atom in a cavity is correlated to the atomic dynamics. Connection between the atomic phases of collapse and revival, and the Wigner function pattern is explored. Initial classical coherent field can evolve into nonclassical field. Schrodinger cat state field is generate during the atomic collapse phase. For initial Schrodinger cat field state, the state dissolves with time but revives during the atomic phase that corresponds with the initial phase. More intricate but orderly characteristics are found between the collapse-revival dynamics and the patterns of the Wigner function for initial thermal field.

arXiv:0812.2615•Dec 14, 2008•0 citations

Wigner quasi-probability distribution for the infinite square well: Energy eigenstates and time-dependent wave packets

M. Belloni, M. A. Doncheski, R. W. Robinett

We calculate and visualize the Wigner quasi-probability distribution for the position and momentum, PW(n)(x,p), for the energy eigenstates of the infinite square well. We evaluate the time-dependent Wigner distribution, PW(x,p;t), for Gaussian wave packet solutions of this system, and illustrate the short-term semi-classical time dependence and the longer-term revival and fractional revival behavior. Our results indicate how the Wigner distribution can be used to examine the highly correlated dynamical position-momentum structure of quantum states. In particular, this tool provides an excellent way of demonstrating the patterns of highly correlated Schrödinger-cat-like “mini-packets” which appear at fractional multiples of the exact revival time.

arXiv:quant-ph/0312086•American Journal of Physics•Aug 13, 2004•35 citations

QUASIPROBABILITY DISTRIBUTIONS FOR THE THREE-LEVEL JAYNES-CUMMINGS MODEL

Nguyen Dinh Huyen, Ho Trung Dung

The Q-function and Wigner function for a three-level system coupled to a one-mode coherent field under two-photon resonance are treated for various initial atomic states. It is shown that the dynamical behavior of the quasiprobability distributions reflects the collapses and revivals in the time histories of the Rabi oscillations in a very interesting way. The structured quasiprobabilities are reviewed in the light of the semiclassical eigenstates.

International Journal of Modern Physics B•Apr 30, 1994•0 citations

Quantum probability distributions in the early Universe. I. Equilibrium properties of the Wigner equation

Frank R. Graziani

This is the first in a series of papers dealing with quantum or Wigner probability distributions and the dynamics of early-Universe phase transitions. In this paper we argue that the inflaton field (a real gauge-singlet scalar field) when spatially averaged over a causal horizon behaves as if it were a dissipative quantum-mechanical system in one dimension. Realizing that the mathematical phase-space or stochastic description of Wigner is the only consistent way to describe these systems and still preserve the canonical commutation relations we devote this paper to investigating various properties of the Wigner formalism. This framework rests on the quasiprobability distribution and its evolution equation: a generalized Fokker-Planck equation. We first show that this generalized Fokker-Planck equation is equivalent to Schr\"odinger's equation for nondissipative pure states. We then show how one computes ground-state energies within this formalism (for nondissipative systems) by calculating ground-state energy levels for a variety of anharmonic potentials. Finally we compute the quantum-mechanical effective potential in one dimension to order g\ensuremath{\Elzxh}.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Aug 15, 1988•24 citations

Quantum tomography on Schwartz space

Tobias Thrien, Gabriele Carcassi, David Carfì +1 more

In this work we show that standard results in quantum tomography, which are typically proven in the context of Hilbert spaces, can analogously be established in the theory of Schwartz spaces. In particular, we will see that quantum states are equivalently characterized by their Wigner function, the characteristic of their Wigner function, and the probability distributions for a family of linear combinations of position and momentum. Physically, the latter can be understood as the evolution of its probability distribution in position over time under, for example, free or harmonic evolution. The result is obtained with techniques that are more accessible to a physicist audience, and shows that, at least for tomography results, the full structure of Hilbert spaces is not necessary.

quant-pharXiv:2611.03521•Nov 3, 2026
Quantum processes can be described in terms of a quasiprobability distribution (the Wigner distribution) analogous to the phase-space probability distribution of the classical realm. In contrast to the incomplete glimpse of the wave function that is achievable in a single shot experiment, the Wigner distribution, accessible by quantum state tomography, reflects the full quantum state. We show that during the fundamental symmetry-breaking process of a generic quantum system, with a symmetry-breaking field driving the quantum system far from equilibrium, the Wigner distribution evolves continuously with the system undergoing a sequence of revivals into the symmetry-unbroken state, followed by collapses onto a quasiclassical state akin to the one realized in infinite-size systems. We show that generically this state is completely delocalized both in momentum and in real space.
We calculate the Wigner quasi-probability distribution for position and momentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite well potential, using both x- and p-space stationary-state solutions, as well as visualizing the results. We then evaluate the time-dependent Wigner distribution, P_W(x,p;t), for Gaussian wave packet solutions of this system, illustrating both the short-term semi-classical time dependence, as well as longer-term revival and fractional revival behavior and the structure during the collapsed state. This tool provides an excellent way of demonstrating the patterns of highly correlated Schrodinger-cat-like `mini-packets' which appear at fractional multiples of the exact revival time.
The transient evolution of nonclassical radiation fields interacting with an atom in a cavity is correlated to the atomic dynamics. Connection between the atomic phases of collapse and revival, and the Wigner function pattern is explored. Initial classical coherent field can evolve into nonclassical field. Schrodinger cat state field is generate during the atomic collapse phase. For initial Schrodinger cat field state, the state dissolves with time but revives during the atomic phase that corresponds with the initial phase. More intricate but orderly characteristics are found between the collapse-revival dynamics and the patterns of the Wigner function for initial thermal field.
We calculate and visualize the Wigner quasi-probability distribution for the position and momentum, PW(n)(x,p), for the energy eigenstates of the infinite square well. We evaluate the time-dependent Wigner distribution, PW(x,p;t), for Gaussian wave packet solutions of this system, and illustrate the short-term semi-classical time dependence and the longer-term revival and fractional revival behavior. Our results indicate how the Wigner distribution can be used to examine the highly correlated dynamical position-momentum structure of quantum states. In particular, this tool provides an excellent way of demonstrating the patterns of highly correlated Schrödinger-cat-like “mini-packets” which appear at fractional multiples of the exact revival time.
This is the first in a series of papers dealing with quantum or Wigner probability distributions and the dynamics of early-Universe phase transitions. In this paper we argue that the inflaton field (a real gauge-singlet scalar field) when spatially averaged over a causal horizon behaves as if it were a dissipative quantum-mechanical system in one dimension. Realizing that the mathematical phase-space or stochastic description of Wigner is the only consistent way to describe these systems and still preserve the canonical commutation relations we devote this paper to investigating various properties of the Wigner formalism. This framework rests on the quasiprobability distribution and its evolution equation: a generalized Fokker-Planck equation. We first show that this generalized Fokker-Planck equation is equivalent to Schr\"odinger's equation for nondissipative pure states. We then show how one computes ground-state energies within this formalism (for nondissipative systems) by calculating ground-state energy levels for a variety of anharmonic potentials. Finally we compute the quantum-mechanical effective potential in one dimension to order g\ensuremath{\Elzxh}.
In this work we show that standard results in quantum tomography, which are typically proven in the context of Hilbert spaces, can analogously be established in the theory of Schwartz spaces. In particular, we will see that quantum states are equivalently characterized by their Wigner function, the characteristic of their Wigner function, and the probability distributions for a family of linear combinations of position and momentum. Physically, the latter can be understood as the evolution of its probability distribution in position over time under, for example, free or harmonic evolution. The result is obtained with techniques that are more accessible to a physicist audience, and shows that, at least for tomography results, the full structure of Hilbert spaces is not necessary.