Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions

A noncommutative extension of an ideal (Hamiltonian) fluid model in $3+1$-dimensions is proposed. The model enjoys several interesting features: it allows a multi-parameter central extension in Galilean boost algebra (which is significant being contrary to existing belief that similar feature can appear only in $2+1$-dim.); noncommutativity generates vorticity in a canonically irrotational fluid; it induces a non-barotropic pressure leading to a non-isentropic system. (Barotropic fluids are entropy preserving as pressure depends only on matter density.) Our fluid model is termed "Exotic" since it has close resemblance with the extensively studied planar (2+1-dim.) Exotic models and Exotic (noncommutative) field theories.Comment: 11 pages, significant extensions with new results on NC induced vorticity and non-barotropy, accepted in PRD (rap.comm.

Note on Morita Inequality for Planar Noncommutative Inverted Oscillator

A recent conjecture of Morita predicts a lower bound in temperature $T$ of a chaotic system, $T\geq (\hbar/2\pi)\Lambda$, $\Lambda$ being the Lyapunov exponent, which was demonstrated for a one dimensional inverse harmonic oscillator. In the present work we discuss the robustness of this demonstration in an extended version of the above model, where the inverse harmonic oscillator lives a in two dimensional noncommutative space. We show that, without noncommutativity, Morita's conjecture survives in an essentially unchanged way in two dimensions. However, if noncommutativity is switched on, the noncommutativity induced correction terms conspire to produce, in classical framework, a purely oscillating non-chaotic system without any exponential growth so that Lyapunov exponent is not defined. On the other hand, following Morita's analysis, we show that quantum mechanically an effective temperature with noncommutative corrections is generated. Thus Morita's conjecture is not applicable in the noncommutative plane. A dimensionless parameter $\sigma =m\alpha\theta^2$, (where $m, \alpha, \theta$ are the particle mass, coupling strength with inverse oscillator and the noncommutative parameter respectively) plays a crucial role in our analysis.Comment: 9 pages, 4 figures, Comments are welcom

Relativistic Spinning Particle in a Non-Commutative Extended Spacetime

The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily constrained and constraint analysis, in the Dirac scheme, is both novel and instructive. Our major finding is an associated novel non-commutative structure in the extended space. This is obtained in a particular gauge. The model possesses a large gauge freedom and hence a judicious choice of gauge becomes imperative. The gauge fixed system in reduced phase space simplifies considerably for further study. We have shown that this non-commutative phase space algebra is essential in revealing the spin effects in the particle model through the Lorentz generator and Hamiltonian equations of motion.Comment: Minor changes, matches published version

Spectral Discontinuities in Constrained Dynamical Models

As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well known relativistic field theory - the chiral Schwinger model. We apply the Hamiltonian constraint analysis of Dirac [1] and find that the nature of constraints depends critically on a $c$-number parameter present in the model. Thus a change in the parameter alters the number of dynamical modes in an abrupt and non-perturbative way. We have obtained new {\it{real}} energy levels for the quantum mechanical model as we explore {\it{complex}} domains in the parameter space. These were forbidden in the parent chiral Schwinger field theory where the analogue Jackiw-Rajaraman parameter is restricted to be real. We explicitly show existence of modes that satisfy higher derivative Pais-Uhlenbeck form of dynamics [3]. We also show that the Cranking Model [7], well known in Nuclear Physics, can be interpreted as a spatially frozen version of another well studied relativistic field theory in 2+1-dimension- the Maxwell-Chern-Simons-Proca Model [8].Comment: laTex, 17 pages, 5 figures, change in title, abstract, paper is rewritten, no changes in final result and conclusion, to appear in J.Phys.

Spontaneous Symmetry Breaking and Landau Phase Transition in Horava Gravity

Presence of higher derivative terms in the Horava model of gravity can generate an instability in the Minkowski ground state. This in turn leads to a space dependent vacuum metric with a length scale determined by the higher derivative coupling coefficient. The translation invariance is spontaneously broken in the process. The phenomenon is interpreted as a form of Landau liquid-solid phase translation. The (metric) condensate acts as a source that modifies the Newtonian potential below the length scale but keeps it unchanged for sufficiently large distance.Comment: 14 pages Late

Towards a Discrete Spacetime

A formalism is proposed to generate (the first step of) a discrete spacetime: spacetime with an inbuilt length scale. We follow the celebrated Landau theory of liquid - solid phase transition induced by Spontaneous Symmetry Breaking by a condensate whose Fourier transform has support at a {\it{non-zero}} momentum. The latter requirement is essential for breaking the translation symmetry. This, in turn, compels us to generalize Einstein action to higher derivative terms.Comment: 7 pages, Latex, Comments are welcom

Persistence in Ferromagnetic Ordering: Dependence upon initial configuration

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions $d=2$ and $3$. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures ($T_f$) below the critical one ($T_{c}$), from different initial temperatures $T_{i} \geq T_{c}$. In long time limit, for $T_{i} > T_{c}$, the persistence probability exhibits power-law decay with exponents $\theta \simeq 0.22$ and $\simeq 0.18$ in $d=2$ and $3$, respectively. For finite $T_i$, the early time behavior is a different power-law whose life-time diverges and exponent decreases as $T_{i} \rightarrow T_{c}$. The crossover length between the two steps diverges as the equilibrium correlation length. $T_i=T_c$ is expected to provide a {\it{new universality class}} for which we obtain $\theta \simeq 0.035$ in $d=2$ and $\simeq 0.10$ in $d=3$. The time dependence of the average domain size $\ell$, however, is observed to be rather insensitive to the choice of $T_i$.Comment: 8 pages, 9 figure

Fractality in Persistence Decay and Domain Growth during Ferromagnetic Ordering: Dependence upon initial correlation

Dynamics of ordering in Ising model, following quench to zero temperature, have been studied via Glauber spin-flip Monte Carlo simulations in space dimensions $d=2$ and $3$. One of the primary objectives has been to understand phenomena associated with the persistent spins, viz., time decay in the number of unaffected spins, growth of the corresponding pattern and its fractal dimensionality, for varying correlation length in the initial configurations, prepared at different temperatures, at and above the critical value. It is observed that the fractal dimensionality and the exponent describing the power-law decay of persistence probability are strongly dependent upon the relative values of nonequilibrium domain size and the initial equilibrium correlation length. Via appropriate scaling analyses, these quantities have been estimated for quenches from infinite and critical temperatures. The above mentioned dependence is observed to be less pronounced in higher dimension. In addition to these findings for the local persistence, we present results for the global persistence as well. Further, important observations on the standard domain growth problem are reported. For the latter, a controversy in $d=3$, related to the value of the exponent for the power-law growth of the average domain size with time, has been resolved.Comment: 10 pages, 16 figure

Kinetics of Vapor-Solid Phase Transitions: Structure, growth and mechanism

Kinetics of separation between the low and high density phases in a single component Lennard-Jones model has been studied via molecular dynamics simulations, at a very low temperature, in the space dimension $d=2$. For densities close to the vapor (low density) branch of the coexistence curve, disconnected clusters of the high density phase exhibit ballistic motion, the kinetic energy distribution of the clusters being closely Maxwellian. Starting from nearly circular shapes, at the time of nucleation, these clusters grow via sticky collisions, gaining filament-like nonequilibrium structure at late times, with a very low fractal dimensionality. The origin of the latter is shown to lie in the low mobility of the constituent particles, in the corresponding cluster reference frame, due to the (quasi-long-range) crystalline order. Standard self-similarity in the domain pattern, typically observed in kinetics of phase transitions, is found to be absent in this growth process. This invalidates the common method, that provides a growth law same as in immiscible solid mixtures, of quantifying growth. An appropriate alternative approach, involving the fractality in the structure, quantifies the growth of the characteristic "length" to be a power-law with time, the exponent being surprisingly high. The observed growth law has been derived via a nonequilibrium kinetic theory.Comment: 5 pages, 4 figure

Domain Coarsening in 2-d Ising Model: Finite-Size Scaling for Conserved Dynamics

We quantify the effect of system size in the kinetics of domain growth in Ising model with 50:50 composition in two spatial dimensions. Our estimate of the exponent, $\alpha=0.334\pm0.004$, for the power law growth of linear domain size, from Monte Carlo simulation using small systems of linear dimensions L=16, 32, 64, and 128, is in excellent agreement with the prediction of Lifshitz-Slyozov (LS) theory, $\alpha=1/3$. We find that the LS exponent sets in very early and continues to be true until average size of domains reaches three quarters of equilibrium limit.Comment: 4 pages, 4 figure