3,135 research outputs found
Vortices in quantum droplets: Analogies between boson and fermion systems
The main theme of this review is the many-body physics of vortices in quantum
droplets of bosons or fermions, in the limit of small particle numbers. Systems
of interest include cold atoms in traps as well as electrons confined in
quantum dots. When set to rotate, these in principle very different quantum
systems show remarkable analogies. The topics reviewed include the structure of
the finite rotating many-body state, universality of vortex formation and
localization of vortices in both bosonic and fermionic systems, and the
emergence of particle-vortex composites in the quantum Hall regime. An overview
of the computational many-body techniques sets focus on the configuration
interaction and density-functional methods. Studies of quantum droplets with
one or several particle components, where vortices as well as coreless vortices
may occur, are reviewed, and theoretical as well as experimental challenges are
discussed.Comment: Review article, 53 pages, 53 figure
Signatures of Wigner Localization in Epitaxially Grown Nanowires
It was predicted by Wigner in 1934 that the electron gas will undergo a
transition to a crystallized state when its density is very low. Whereas
significant progress has been made towards the detection of electronic Wigner
states, their clear and direct experimental verification still remains a
challenge. Here we address signatures of Wigner molecule formation in the
transport properties of InSb nanowire quantum dot systems, where a few
electrons may form localized states depending on the size of the dot (i.e. the
electron density). By a configuration interaction approach combined with an
appropriate transport formalism, we are able to predict the transport
properties of these systems, in excellent agreement with experimental data. We
identify specific signatures of Wigner state formation, such as the strong
suppression of the antiferromagnetic coupling, and are able to detect the onset
of Wigner localization, both experimentally and theoretically, by studying
different dot sizes.Comment: 4 pages, 4 figure
Equilibration of isolated macroscopic quantum systems
We investigate the equilibration of an isolated macroscopic quantum system in
the sense that deviations from a steady state become unmeasurably small for the
overwhelming majority of times within any sufficiently large time interval. The
main requirements are that the initial state, possibly far from equilibrium,
exhibits a macroscopic population of at most one energy level and that
degeneracies of energy eigenvalues and of energy gaps (differences of energy
eigenvalues) are not of exceedingly large multiplicities. Our approach closely
follows and extends recent works by Short and Farrelly [2012 New J. Phys. 14
013063], in particular going beyond the realm of finite-dimensional systems and
large effective dimensions.Comment: 19 page
Thermal ratchet effects in ferrofluids
Rotational Brownian motion of colloidal magnetic particles in ferrofluids
under the influence of an oscillating external magnetic field is investigated.
It is shown that for a suitable time dependence of the magnetic field, a noise
induced rotation of the ferromagnetic particles due to rectification of thermal
fluctuations takes place. Via viscous coupling, the associated angular momentum
is transferred from the magnetic nano-particles to the carrier liquid and can
then be measured as macroscopic torque on the fluid sample. A thorough
theoretical analysis of the effect in terms of symmetry considerations,
analytical approximations, and numerical solutions is given which is in
accordance with recent experimental findings.Comment: 18 pages, 6 figure
Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean field approach
We address a recently introduced model describing a system of periodically
coupled nonlinear phase oscillators submitted to multiplicative white noises,
wherein a ratchet-like transport mechanism arises through a symmetry-breaking
noise-induced nonequilibrium phase transition. Numerical simulations of this
system reveal amazing novel features such as negative zero-bias conductance and
anomalous hysteresis, explained resorting to a strong-coupling analysis in the
thermodynamic limit. Using an explicit mean-field approximation we explore the
whole ordered phase finding a transition from anomalous to normal hysteresis
inside this phase, estimating its locus and identifying (within this scheme) a
mechanism whereby it takes place.Comment: RevTex, 21 pgs, 15 figures. Submited to Physical Review E (2000
Nonequilibrium coupled Brownian phase oscillators
A model of globally coupled phase oscillators under equilibrium (driven by
Gaussian white noise) and nonequilibrium (driven by symmetric dichotomic
fluctuations) is studied. For the equilibrium system, the mean-field state
equation takes a simple form and the stability of its solution is examined in
the full space of order parameters. For the nonequilbrium system, various
asymptotic regimes are obtained in a closed analytical form. In a general case,
the corresponding master equations are solved numerically. Moreover, the
Monte-Carlo simulations of the coupled set of Langevin equations of motion is
performed. The phase diagram of the nonequilibrium system is presented. For the
long time limit, we have found four regimes. Three of them can be obtained from
the mean-field theory. One of them, the oscillating regime, cannot be predicted
by the mean-field method and has been detected in the Monte-Carlo numerical
experiments.Comment: 9 pages 8 figure
Quantization and Corrections of Adiabatic Particle Transport in a Periodic Ratchet Potential
We study the transport of an overdamped particle adiabatically driven by an
asymmetric potential which is periodic in both space and time. We develop an
adiabatic perturbation theory after transforming the Fokker-Planck equation
into a time-dependent hermitian problem, and reveal an analogy with quantum
adiabatic particle transport. An analytical expression is obtained for the
ensemble average of the particle velocity in terms of the Berry phase of the
Bloch states. Its time average is shown to be quantized as a Chern number in
the deterministic or tight-binding limit, with exponentially small corrections.
In the opposite limit, where the thermal energy dominates the ratchet
potential, a formula for the average velocity is also obtained, showing a
second order dependence on the potential.Comment: 8 page
Phase transitions in optimal unsupervised learning
We determine the optimal performance of learning the orientation of the
symmetry axis of a set of P = alpha N points that are uniformly distributed in
all the directions but one on the N-dimensional sphere. The components along
the symmetry breaking direction, of unitary vector B, are sampled from a
mixture of two gaussians of variable separation and width. The typical optimal
performance is measured through the overlap Ropt=B.J* where J* is the optimal
guess of the symmetry breaking direction. Within this general scenario, the
learning curves Ropt(alpha) may present first order transitions if the clusters
are narrow enough. Close to these transitions, high performance states can be
obtained through the minimization of the corresponding optimal potential,
although these solutions are metastable, and therefore not learnable, within
the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper
contains one new section, Bayesian versus optimal solutions, where we explain
in detail the results supporting our claim that bayesian learning may not be
optimal. Figures 4 of the first submission was difficult to understand. We
replaced it by two new figures (Figs. 4 and 5 in this new version) containing
more detail
Transport and interaction blockade of cold bosonic atoms in a triple-well potential
We theoretically investigate the transport properties of cold bosonic atoms
in a quasi one-dimensional triple-well potential that consists of two large
outer wells, which act as microscopic source and drain reservoirs, and a small
inner well, which represents a quantum-dot-like scattering region. Bias and
gate "voltages" introduce a time-dependent tilt of the triple-well
configuration, and are used to shift the energetic level of the inner well with
respect to the outer ones. By means of exact diagonalization considering a
total number of six atoms in the triple-well potential, we find diamond-like
structures for the occurrence of single-atom transport in the parameter space
spanned by the bias and gate voltages. We discuss the analogy with Coulomb
blockade in electronic quantum dots, and point out how one can infer the
interaction energy in the central well from the distance between the diamonds.Comment: 18 pages, 6 figure
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