---
_id: '7638'
abstract:
- lang: eng
  text: Following on from our recent work, we investigate a stochastic approach to
    non-equilibrium quantum spin systems. We show how the method can be applied to
    a variety of physical observables and for different initial conditions. We provide
    exact formulae of broad applicability for the time-dependence of expectation values
    and correlation functions following a quantum quench in terms of averages over
    classical stochastic processes. We further explore the behavior of the classical
    stochastic variables in the presence of dynamical quantum phase transitions, including
    results for their distributions and correlation functions. We provide details
    on the numerical solution of the associated stochastic differential equations,
    and examine the growth of fluctuations in the classical description. We discuss
    the strengths and limitations of the current implementation of the stochastic
    approach and the potential for further development.
article_number: '013106'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Stefano
  full_name: De Nicola, Stefano
  id: 42832B76-F248-11E8-B48F-1D18A9856A87
  last_name: De Nicola
  orcid: 0000-0002-4842-6671
- first_name: B.
  full_name: Doyon, B.
  last_name: Doyon
- first_name: M. J.
  full_name: Bhaseen, M. J.
  last_name: Bhaseen
citation:
  ama: 'De Nicola S, Doyon B, Bhaseen MJ. Non-equilibrium quantum spin dynamics from
    classical stochastic processes. <i>Journal of Statistical Mechanics: Theory and
    Experiment</i>. 2020;2020(1). doi:<a href="https://doi.org/10.1088/1742-5468/ab6093">10.1088/1742-5468/ab6093</a>'
  apa: 'De Nicola, S., Doyon, B., &#38; Bhaseen, M. J. (2020). Non-equilibrium quantum
    spin dynamics from classical stochastic processes. <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/ab6093">https://doi.org/10.1088/1742-5468/ab6093</a>'
  chicago: 'De Nicola, Stefano, B. Doyon, and M. J. Bhaseen. “Non-Equilibrium Quantum
    Spin Dynamics from Classical Stochastic Processes.” <i>Journal of Statistical
    Mechanics: Theory and Experiment</i>. IOP Publishing, 2020. <a href="https://doi.org/10.1088/1742-5468/ab6093">https://doi.org/10.1088/1742-5468/ab6093</a>.'
  ieee: 'S. De Nicola, B. Doyon, and M. J. Bhaseen, “Non-equilibrium quantum spin
    dynamics from classical stochastic processes,” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>, vol. 2020, no. 1. IOP Publishing, 2020.'
  ista: 'De Nicola S, Doyon B, Bhaseen MJ. 2020. Non-equilibrium quantum spin dynamics
    from classical stochastic processes. Journal of Statistical Mechanics: Theory
    and Experiment. 2020(1), 013106.'
  mla: 'De Nicola, Stefano, et al. “Non-Equilibrium Quantum Spin Dynamics from Classical
    Stochastic Processes.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>,
    vol. 2020, no. 1, 013106, IOP Publishing, 2020, doi:<a href="https://doi.org/10.1088/1742-5468/ab6093">10.1088/1742-5468/ab6093</a>.'
  short: 'S. De Nicola, B. Doyon, M.J. Bhaseen, Journal of Statistical Mechanics:
    Theory and Experiment 2020 (2020).'
corr_author: '1'
date_created: 2020-04-05T22:00:50Z
date_published: 2020-01-22T00:00:00Z
date_updated: 2026-04-02T14:33:33Z
day: '22'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1088/1742-5468/ab6093
ec_funded: 1
external_id:
  arxiv:
  - '1909.13142'
  isi:
  - '000520187500001'
file:
- access_level: open_access
  checksum: 4030e683c15d30b7b4794ec7dc1b6537
  content_type: application/pdf
  creator: dernst
  date_created: 2020-04-06T13:15:49Z
  date_updated: 2020-07-14T12:48:01Z
  file_id: '7648'
  file_name: 2020_JournStatisticalMech_DeNicola.pdf
  file_size: 3159026
  relation: main_file
file_date_updated: 2020-07-14T12:48:01Z
has_accepted_license: '1'
intvolume: '      2020'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
  eissn:
  - 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Non-equilibrium quantum spin dynamics from classical stochastic processes
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 2020
year: '2020'
...
---
_id: '6840'
abstract:
- lang: eng
  text: "We discuss thermodynamic properties of harmonically trapped\r\nimperfect
    quantum gases. The spatial inhomogeneity of these systems imposes\r\na redefinition
    of the mean-field interparticle potential energy as compared\r\nto the homogeneous
    case. In our approach, it takes the form a\r\n2N2 ωd, where\r\nN is the number
    of particles, ω—the harmonic trap frequency, d—system’s\r\ndimensionality, and
    a is a parameter characterizing the interparticle interaction.\r\nWe provide arguments
    that this model corresponds to the limiting case of\r\na long-ranged interparticle
    potential of vanishingly small amplitude. This\r\nconclusion is drawn from a computation
    similar to the well-known Kac scaling\r\nprocedure, which is presented here in
    a form adapted to the case of an isotropic\r\nharmonic trap. We show that within
    the model, the imperfect gas of trapped\r\nrepulsive bosons undergoes the Bose–Einstein
    condensation provided d > 1.\r\nThe main result of our analysis is that in d =
    1 the gas of attractive imperfect\r\nfermions with a = −aF < 0 is thermodynamically
    equivalent to the gas of\r\nrepulsive bosons with a = aB > 0 provided the parameters
    aF and aB fulfill\r\nthe relation aB + aF = \x1F. This result supplements similar
    recent conclusion\r\nabout thermodynamic equivalence of two-dimensional (2D) uniform
    imperfect\r\nrepulsive Bose and attractive Fermi gases."
article_number: '063101'
article_processing_charge: No
arxiv: 1
author:
- first_name: Krzysztof
  full_name: Mysliwy, Krzysztof
  id: 316457FC-F248-11E8-B48F-1D18A9856A87
  last_name: Mysliwy
- first_name: Marek
  full_name: Napiórkowski, Marek
  last_name: Napiórkowski
citation:
  ama: 'Mysliwy K, Napiórkowski M. Thermodynamics of inhomogeneous imperfect quantum
    gases in harmonic traps. <i>Journal of Statistical Mechanics: Theory and Experiment</i>.
    2019;2019(6). doi:<a href="https://doi.org/10.1088/1742-5468/ab190d">10.1088/1742-5468/ab190d</a>'
  apa: 'Mysliwy, K., &#38; Napiórkowski, M. (2019). Thermodynamics of inhomogeneous
    imperfect quantum gases in harmonic traps. <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/ab190d">https://doi.org/10.1088/1742-5468/ab190d</a>'
  chicago: 'Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous
    Imperfect Quantum Gases in Harmonic Traps.” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOP Publishing, 2019. <a href="https://doi.org/10.1088/1742-5468/ab190d">https://doi.org/10.1088/1742-5468/ab190d</a>.'
  ieee: 'K. Mysliwy and M. Napiórkowski, “Thermodynamics of inhomogeneous imperfect
    quantum gases in harmonic traps,” <i>Journal of Statistical Mechanics: Theory
    and Experiment</i>, vol. 2019, no. 6. IOP Publishing, 2019.'
  ista: 'Mysliwy K, Napiórkowski M. 2019. Thermodynamics of inhomogeneous imperfect
    quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and
    Experiment. 2019(6), 063101.'
  mla: 'Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous
    Imperfect Quantum Gases in Harmonic Traps.” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>, vol. 2019, no. 6, 063101, IOP Publishing, 2019, doi:<a
    href="https://doi.org/10.1088/1742-5468/ab190d">10.1088/1742-5468/ab190d</a>.'
  short: 'K. Mysliwy, M. Napiórkowski, Journal of Statistical Mechanics: Theory and
    Experiment 2019 (2019).'
date_created: 2019-09-01T22:00:59Z
date_published: 2019-06-13T00:00:00Z
date_updated: 2025-03-31T16:01:18Z
day: '13'
department:
- _id: RoSe
doi: 10.1088/1742-5468/ab190d
ec_funded: 1
external_id:
  arxiv:
  - '1810.02209'
  isi:
  - '000471650100001'
intvolume: '      2019'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1810.02209
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '665385'
  name: International IST Doctoral Program
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
  eissn:
  - 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2019
year: '2019'
...