Search results for "Classical limit"
showing 10 items of 28 documents
Quantum and Classical Statistical Mechanics of the Integrable Models in 1 + 1 Dimensions
1990
In a short but remarkable paper Yang and Yang [1] showed that the free energy of a model system consisting of N bosons on a line with repulsive δ-function interactions was given by a set of coupled integral equations. The Yangs’ chosen model is in fact the repulsive version of the quantum Nonlinear Schrodinger (NLS) model. We have shown that with appropriate extensions and different dispersion relations and phase shifts similar formulae apply to ‘all’ of the integrable models quantum or classical. These models include the sine-Gordon (s-G) and sinh-Gordon (sinh-G) models, the two NLS models (attractive and repulsive), the Landau-Lifshitz (L-L’) model which includes all four previous models,…
On the convexity of Relativistic Hydrodynamics
2013
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\it Rev. Mod. Phys.} {\bf 61} 75). The classical limit is recovered.
On the physical contents of q-deformed Minkowski spaces
1994
Some physical aspects of $q$-deformed spacetimes are discussed. It is pointed out that, under certain standard assumptions relating deformation and quantization, the classical limit (Poisson bracket description) of the dynamics is bound to contain unusual features. At the same time, it is argued that the formulation of an associated $q$-deformed field theory is fraught with serious difficulties.
Quantum corrections to inflation: the importance of RG-running and choosing the optimal RG-scale
2017
We demonstrate the importance of correctly implementing RG running and choosing the RG scale when calculating quantum corrections to inflaton dynamics. We show that such corrections are negligible for single-field inflation, in the sense of not altering the viable region in the ${n}_{s}\ensuremath{-}r$ plane, when imposing Planck constraints on ${A}_{s}$. Surprisingly, this also applies, in a nontrivial way, for an inflaton coupled to additional spectator degrees of freedom. The result relies on choosing the renormalization scale (pseudo-)optimally, thereby avoiding unphysical large logarithmic corrections to the Friedmann equations and large running of the couplings. We find that the viabl…
Quantum effects in the capture of charged particles by dipolar polarizable symmetric top molecules. I. General axially nonadiabatic channel treatment
2013
The rate coefficients for capture of charged particles by dipolar polarizable symmetric top molecules in the quantum collision regime are calculated within an axially nonadiabatic channel approach. It uses the adiabatic approximation with respect to rotational transitions of the target within first-order charge-dipole interaction and takes into account the gyroscopic effect that decouples the intrinsic angular momentum from the collision axis. The results are valid for a wide range of collision energies (from single-wave capture to the classical limit) and dipole moments (from the Vogt-Wannier and fly-wheel to the adiabatic channel limit).
Statistical Mechanics of the sine-Gorden Field: Part II
1985
From the work of the Part I we are now in a position to address ourselves to the main problem posed in these lectures — the evaluation of Z, (1.11), for the s-G field after canonical transformation to the action-angle variables (4.27).
Quantization as a consequence of the group law
1982
A method of gemetric quantization which solely makes use of the structure of the symmetry group of the dynamical system is proposed; the classical limit is discussed along similar lines. The method is applied to two examples, the free particle and the harmonic oscillator.
On the semiclassical limit of the defocusing Davey-Stewartson II equation
2018
Inverse scattering is the most powerful tool in theory of integrable systems. Starting in the late sixties resounding great progress was made in (1+1) dimensional problems with many break-through results as on soliton interactions. Naturally the attention in recent years turns towards higher dimensional problems as the Davey-Stewartson equations, an integrable generalisation of the (1+1)-dimensionalcubic nonlinear Schrödinger equation. The defocusing Davey-Stewartson II equation, in its semi-classical limit has been shown in numerical experiments to exhibit behavior that qualitatively resembles that of its one-dimensional reduction, namely the generation of a dispersive shock wave: smooth i…
On a possible origin of quantum groups
1991
A Poisson bracket structure having the commutation relations of the quantum group SLq(2) is quantized by means of the Moyal star-product on C∞(ℝ2), showing that quantum groups are not exactly quantizations, but require a quantization (with another parameter) in the background. The resulting associative algebra is a strongly invariant nonlinear star-product realization of the q-algebra Uq(sl(2)). The principle of strong invariance (the requirement that the star-commutator is star-expressed, up to a phase, by the same function as its classical limit) implies essentially the uniqueness of the commutation relations of Uq(sl(2)).
Strain gradient plasticity, strengthening effects and plastic limit analysis
2010
Abstract Within the framework of isotropic strain gradient plasticity, a rate-independent constitutive model exhibiting size dependent hardening is formulated and discussed with particular concern to its strengthening behavior. The latter is modelled as a (fictitious) isotropic hardening featured by a potential which is a positively degree-one homogeneous function of the effective plastic strain and its gradient. This potential leads to a strengthening law in which the strengthening stress, i.e. the increase of the plastically undeformed material initial yield stress, is related to the effective plastic strain through a second order PDE and related higher order boundary conditions. The plas…