37 research outputs found
Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
We investigate the relaxation dynamics of the integrable Lieb-Liniger model
of contact-interacting bosons in one dimension following a sudden quench of the
collisional interaction strength. The system is initially prepared in its
noninteracting ground state and the interaction strength is then abruptly
switched to a positive value, corresponding to repulsive interactions between
the bosons. We calculate equal-time correlation functions of the nonequilibrium
Bose field for small systems of up to five particles via symbolic evaluation of
coordinate Bethe-ansatz expressions for operator matrix elements between
Lieb-Liniger eigenstates. We characterize the relaxation of the system by
comparing the time-evolving correlation functions following the quench to the
equilibrium correlations predicted by the diagonal ensemble and relate the
behavior of these correlations to that of the quantum fidelity between the
many-body wave function and the initial state of the system. Our results for
the asymptotic scaling of local second-order correlations with increasing
interaction strength agree with the predictions of recent generalized
thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations
obtained within our approach exhibit a markedly different power-law dependence
on the interaction strength as the Tonks-Girardeau limit of infinitely strong
interactions is approached.Comment: 19 pages, 10 figures. v3: Final version. Typos fixed, and other minor
change
Reconciling the Classical-Field Method with the Beliaev Broken Symmetry Approach
We present our views on the issues raised in the chapter by Griffin and
Zaremba [A. Griffin and E. Zaremba, in Quantum Gases: Finite Temperature and
Non-Equilibrium Dynamics, N. P. Proukakis, S. A. Gardiner, M. J. Davis, and M.
H. Szymanska, eds., Imperial College Press, London (in press)]. We review some
of the strengths and limitations of the Bose symmetry-breaking assumption, and
explain how such an approach precludes the description of many important
phenomena in degenerate Bose gases. We discuss the theoretical justification
for the classical-field (c-field) methods, their relation to other
non-perturbative methods for similar systems, and their utility in the
description of beyond-mean-field physics. Although it is true that present
implementations of c-field methods cannot accurately describe certain
collective oscillations of the partially condensed Bose gas, there is no
fundamental reason why these methods cannot be extended to treat such
scenarios. By contrast, many regimes of non-equilibrium dynamics that can be
described with c-field methods are beyond the reach of generalised mean-field
kinetic approaches based on symmetry-breaking, such as the ZNG formalism.Comment: 8 pages. Unedited version of chapter to appear in Quantum Gases:
Finite Temperature and Non-Equilibrium Dynamics (Vol. 1 Cold Atoms Series).
N.P. Proukakis, S.A. Gardiner, M.J. Davis and M.H. Szymanska, eds. Imperial
College Press, London (in press). See
http://www.icpress.co.uk/physics/p817.html v2: Added arXiv cross-reference
C-Field Methods for Non-Equilibrium Bose Gases
We review c-field methods for simulating the non-equilibrium dynamics of
degenerate Bose gases beyond the mean-field Gross-Pitaevskii approximation. We
describe three separate approaches that utilise similar numerical methods, but
have distinct regimes of validity. Systems at finite temperature can be treated
with either the closed-system projected Gross-Pitaevskii equation (PGPE), or
the open-system stochastic projected Gross-Pitaevskii equation (SPGPE). These
are both applicable in quantum degenerate regimes in which thermal fluctuations
are significant. At low or zero temperature, the truncated Wigner projected
Gross-Pitaevskii equation (TWPGPE) allows for the simulation of systems in
which spontaneous collision processes seeded by quantum fluctuations are
important. We describe the regimes of validity of each of these methods, and
discuss their relationships to one another, and to other simulation techniques
for the dynamics of Bose gases. The utility of the SPGPE formalism in modelling
non-equilibrium Bose gases is illustrated by its application to the dynamics of
spontaneous vortex formation in the growth of a Bose-Einstein condensate.Comment: 7 pages, 1 figure. Unedited version of chapter to appear in Quantum
Gases: Finite Temperature and Non-Equilibrium Dynamics (Vol. 1 Cold Atoms
Series). N.P. Proukakis, S.A. Gardiner, M.J. Davis and M.H. Szymanska, eds.
Imperial College Press, London (in press). See
http://www.icpress.co.uk/physics/p817.html v2: Added arXiv cross-reference
The incidence of skin cancer in relation to climate change in South Africa
Abstract: Please refer to full text to view abstract
Condensation and quasicondensation in an elongated three-dimensional Bose gas
We study the equilibrium correlations of a Bose gas in an elongated three-dimensional harmonic trap using a grand-canonical classical-field method. We focus in particular on the progressive transformation of the gas from the normal phase, through a phase-fluctuating quasicondensate regime to the so-called true-condensate regime, with decreasing temperature. Choosing realistic experimental parameters, we quantify the density fluctuations and phase coherence of the atomic field as functions of the system temperature. We identify the onset of Bose condensation through analysis of both the generalized Binder cumulant appropriate to the inhomogeneous system, and the suppression of the effective many-body T matrix that characterizes interactions between condensate atoms in the finite-temperature field. We find that the system undergoes a second-order transition to condensation near the critical temperature for an ideal Bose gas in the strongly anisotropic three-dimensional geometry but remains in a strongly phase-fluctuating quasicondensate regime until significantly lower temperatures. We characterize the crossover from a quasicondensate to a true condensate by a qualitative change in the form of the nonlocal first-order coherence function of the field and compare our results to those of previous works employing a density-phase Bogoliubov-de Gennes analysis
Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.
Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14路2 per cent (646 of 4544) and the 30-day mortality rate was 1路8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7路61, 95 per cent c.i. 4路49 to 12路90; P < 0路001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0路65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability