Related papers: Multiple-scale approach for the expansion scaling …
The evolution of quantum gases, released from traps, are studied through hydrodynamics, both analytically and numerically, in one and two dimensions. In particular, we demonstrate the existence of long time self-similar solutions of the…
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
In this article, a method is proposed to spatially scale up a trapped ultracold gas while conserving the quantum correlations of the initial many-body state. For systems supporting self-similar dynamics, this is achieved by implementing a…
We prove that the two fluid Landau hydrodynamic equations, when applied to a gas interacting with infinite scattering length (unitary gas) in the presence of harmonic trapping, admit exact scaling solutions of mixed compressional and…
We work out the effective scaling approach to frictionless quantum quenches in a one-dimensional Bose gas trapped in a harmonic trap. The effective scaling approach produces an auxiliary equation for the scaling parameter interpolating…
A truncated Hilbert expansion with multiple scales is used to construct asymptotic solution of the linearized one-dimensional Boltzmann equation with small Knudsen number. The freedom ganed by introducing new independent time variables is…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
A differential geometric approach to singular perturbation theory is presented. It is shown that singular perturbation problems such as multiple-scale and boundary layer problems can be treated more easily on a differential geometric basis.…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
We propose a semiclassical approach to calculate multiparticle cross sections in scalar theories, which have been strongly argued to have the exponential form $\exp(\lambda^{-1}F(\lambda n,\epsilon))$ in the regime $\lambda\to0$, $\lambda…
We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large $t$, well defined scaling properties. We suggest a general…
We address theoretically the puzzling similarity observed in the thermodynamic behaviour of independent clouds of cold dipolar excitons in coupled semiconductor quantum wells. We argue that the condensation of self-trapped exciton gas…
In this paper, we combine the method of multiple scales and the method of matched asymptotic expansions to construct uniformly-valid asymptotic solutions to autonomous and non-autonomous difference equations in the neighbourhood of a…
The non-equilibrium thermodynamics of a gas inside a piston is a conceptually simple problem where analytic results are rare. For example, it is hard to find in the literature analytic formulas that describe the heat exchanged with the…
Using the gradient expansion approach, we formulate a nonlinear cosmological perturbation theory on super-horizon scales valid to $O(\epsilon^2)$, where $\epsilon$ is the expansion parameter associated with a spatial derivative. For…
For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the…
We formulate nonlinear perturbations of a scalar field dominated universe on super-horizon scales. We consider the case of a single scalar field. We take the gradient expansion approach. We adopt the uniform Hubble slicing and derive the…
A late time asymptotic perturbative analysis of curvature coupled complex scalar field models with accelerated cosmological expansion is carried out on the level of formal power series expansions. For this, algebraic analogues of the…
Turbulent scaling phenomena are studied in an ultracold Bose gas away from thermal equilibrium. Fixed points of the dynamical evolution are characterized in terms of universal scaling exponents of correlation functions. The scaling behavior…