1,957 research outputs found
Solitons in a photonic nonlinear quantum walk: lessons from the continuum
We analyse a nonlinear QW model which can be experimentally implemented using
the components of the electric field on an optical nonlinear Kerr medium, which
translates into a rotation in the coin operator, with an angle which depends
(in a nonlinear fashion) on the state of the walker. This simple dependence
makes it easy to consider the space-time continuum limit of the evolution
equation, which takes the form of a nonlinear Dirac equation. The analysis of
this continuum limit allows us, under some approximations, to gain some insight
into the nature of soliton structures, which is illustrated by our numerical
calculations. These solitons are stable structures whose trajectories can be
modulated by choosing the appropriate initial conditions. We have also studied
the stability of solitons when they are subject to an additional phase that
simulates an external electric field, and also explored if they are formed in
higher dimensional spaces
Recommended from our members
Interplay of Analysis and Probability in Physics
The main purpose of this workshop was to foster interaction between researchers in the fields of analysis and probability with the aim of joining forces to understand difficult problems from physics rigorously. 52 researchers of all age groups and from many parts of Europe and overseas attended. The talks and discussions evolved around five topics on the interface between analysis and probability. The main goal of the workshop, the systematic encouragement of intense discussions between the two communities, was achieved to a high extent
L\'evy walks
Random walk is a fundamental concept with applications ranging from quantum
physics to econometrics. Remarkably, one specific model of random walks appears
to be ubiquitous across many fields as a tool to analyze transport phenomena in
which the dispersal process is faster than dictated by Brownian diffusion. The
L\'{e}vy walk model combines two key features, the ability to generate
anomalously fast diffusion and a finite velocity of a random walker. Recent
results in optics, Hamiltonian chaos, cold atom dynamics, bio-physics, and
behavioral science demonstrate that this particular type of random walks
provides significant insight into complex transport phenomena. This review
provides a self-consistent introduction to L\'{e}vy walks, surveys their
existing applications, including latest advances, and outlines further
perspectives.Comment: 50 page
The Stochastic Toolbox User's Guide -- xSPDE3: extensible software for stochastic ordinary and partial differential equations
The xSPDE toolbox treats stochastic partial and ordinary differential
equations, with applications in biology, chemistry, engineering, medicine,
physics and quantum technologies. It computes statistical averages, including
time-step and/or sampling error estimation. xSPDE can provide higher order
convergence, Fourier spectra and probability densities. The toolbox has
graphical output and statistics, as well as weighted, projected, or
forward-backward equations. It can generate input-output quantum spectra. All
equations may have independent periodic, Dirichlet, and Neumann or Robin
boundary conditions in any dimension, for any vector field component, and at
either end of any interval.Comment: User manual for xSPDE software on Github, at
https://github.com/peterddrummond/xspde_matlab. Total of 160 pages with
examples. This is a replacement with minor corrections and an updated
reference list. Accepted, and will appear in Scipos
Pseudo-laminar chaos from on-off intermittency
In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems
one can find diffusive trajectories, which share their appearance with that of
laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from
delay systems with lag-time modulation. Applying, however, to such systems a
test for laminar chaos, as proposed in [Phys. Rev. E 101, 032213 (2020)], these
signals fail such test, thus leading to the notion of pseudo-laminar chaos. The
latter can be interpreted as integrated periodically driven on-off
intermittency. We demonstrate that, on a signal level, true laminar and
pseudo-laminar chaos are hardly distinguishable in systems with and without
dynamical noise. However, very pronounced differences become apparent when
correlations of signals and increments are considered. We compare and contrast
these properties of pseudo-laminar chaos with true laminar chaos.Comment: 13 pages, 7 figure
Dynamics in Cold Atomic Gases: Resonant Behaviour of the Quantum Delta-Kicked Accelerator and Bose-Einstein Condensates in Ring Traps
In this thesis, the dynamics of cold, trapped atomic gases are investigated, and the prospects for exploiting their nonlinear dynamics for inertial sensing are discussed.
In the first part, the resonant and antiresonant dynamics of the atom-optical quantum delta-kicked accelerator with an initial symmetric momentum distribution are considered. The system is modelled as an ideal, non-interacting atomic gas, with a temperature-dependence governed by the width of the initial momentum distribution. The existence of resonant and antiresonant behaviour is established, and analytic expressions describing the dynamics of momentum moments of the time-evolved momentum distribution are derived. In particular, the momentum moment dynamics in both the resonant and antiresonant regimes depend strongly on the width of the initial momentum distribution. The resonant dynamics of all even-ordered momentum moments are shown to exhibit a power-law growth with an exponent given by the order of the moment in the zero-temperature regime, whereas for a broad, thermal initial momentum distribution the exponent is reduced by one. The cross-over in the intermediate regime is also examined, and a characteristic time is determined up to which the system exhibits dynamics associated with the zero-temperature regime. A similar analysis is made for the temperature-dependence of the antiresonant dynamics. This general behaviour is demonstrated explicitly by considering a Maxwell-Boltzmann and uniform momentum distribution, allowing exact expressions describing the dynamics of the second- and fourth-order momentum moments, and momentum cumulants, to be obtained. The relevance of these results to the potential of using this system in accurate determinations of the local gravitational acceleration is discussed.
In the second part, the dynamics of one- and two-component Bose-Einstein Condensates prepared in a counter-rotating superposition of flows in a quasi-1D toroidal trap are studied. Particular attention is paid to the dynamical stability of the initial state in the presence of atom-atom interactions, included via a mean-field description within the Gross-Pitaevskii equation. A broad regime of dynamical stability using a two-component BEC is identified, in which a typical implementation using Rb-87 is predicted to lie. A proof-of-principle Sagnac atom-interferometer using a two-component Rb-87 BEC is then presented, and the accumulation of the Sagnac phase is shown to be possible via relative population measurement or, alternatively, through the continuous monitoring the precession of atomic density fringes. In contrast to conventional Sagnac interferometers, the accumulation of the Sagnac phase is independent of the enclosed area of the interferometer. The prospects of using this system for high-precision determinations of rotation is discussed
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