@article{7638,
  abstract     = {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.},
  author       = {De Nicola, Stefano and Doyon, B. and Bhaseen, M. J.},
  issn         = {1742-5468},
  journal      = {Journal of Statistical Mechanics: Theory and Experiment},
  number       = {1},
  publisher    = {IOP Publishing},
  title        = {{Non-equilibrium quantum spin dynamics from classical stochastic processes}},
  doi          = {10.1088/1742-5468/ab6093},
  volume       = {2020},
  year         = {2020},
}

@article{6840,
  abstract     = {We discuss thermodynamic properties of harmonically trapped
imperfect quantum gases. The spatial inhomogeneity of these systems imposes
a redefinition of the mean-field interparticle potential energy as compared
to the homogeneous case. In our approach, it takes the form a
2N2 ωd, where
N is the number of particles, ω—the harmonic trap frequency, d—system’s
dimensionality, and a is a parameter characterizing the interparticle interaction.
We provide arguments that this model corresponds to the limiting case of
a long-ranged interparticle potential of vanishingly small amplitude. This
conclusion is drawn from a computation similar to the well-known Kac scaling
procedure, which is presented here in a form adapted to the case of an isotropic
harmonic trap. We show that within the model, the imperfect gas of trapped
repulsive bosons undergoes the Bose–Einstein condensation provided d > 1.
The main result of our analysis is that in d = 1 the gas of attractive imperfect
fermions with a = −aF < 0 is thermodynamically equivalent to the gas of
repulsive bosons with a = aB > 0 provided the parameters aF and aB fulfill
the relation aB + aF = . This result supplements similar recent conclusion
about thermodynamic equivalence of two-dimensional (2D) uniform imperfect
repulsive Bose and attractive Fermi gases.},
  author       = {Mysliwy, Krzysztof and Napiórkowski, Marek},
  issn         = {1742-5468},
  journal      = {Journal of Statistical Mechanics: Theory and Experiment},
  number       = {6},
  publisher    = {IOP Publishing},
  title        = {{Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps}},
  doi          = {10.1088/1742-5468/ab190d},
  volume       = {2019},
  year         = {2019},
}