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ABSTRACT: We study dynamic field theories for nonconserving N-vector models that are subject to spatial-anisotropic bias perturbations. We first investigate the conditions under which these field theories can have a single length scale. When N=2 or N≥4, it turns out that there are no such field theories and, hence, the corresponding models are pushed by the bias into the Ising class. We further construct nontrivial field theories for the N=3 case with certain bias perturbations and analyze the renormalization-group flow equations. We find that the three-component systems can exhibit rich critical behavior belonging to two different universality classes.
Physical Review E 01/2011; 83(1 Pt 1):011117. · 2.26 Impact Factor
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ABSTRACT: We study dynamic field theories for nonconserving $N$-vector models that are
subject to spatial-anisotropic bias perturbations. We first investigate the
conditions under which these field theories can have a single length scale.
When N=2 or $N \ge 4$, it turns out that there are no such field theories, and,
hence, the corresponding models are pushed by the bias into the Ising class. We
further construct nontrivial field theories for N=3 case with certain bias
perturbations and analyze the renormalization-group flow equations. We find
that the three-component systems can exhibit rich critical behavior belonging
to two different universality classes.
12/2008;
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ABSTRACT: We bosonize (2+1)-dimensional fermionic theory using coherent states. The gauge-invariant subspace of boson-Chern-Simons Hilbert space is mapped to fermionic Hilbert space. This subspace is then equipped with a coherent state basis. These coherent states are labelled by a dynamic spinor field. The label manifold could be assigned a physical meaning in terms of density and spin density. A path-integral representation of the evolution operator in terms of these physical variables is given. The corresponding classical theory when restricted to LLL is described by spin fluctuations alone and is found to be the NLSM with Hopf term. The formalism developed here is suitable to study quantum Hall skyrmions semiclassically and/or beyond the hydrodynamic limit. The effects of Landau level mixing or the presence of slowly varying external fields can also be easily incorporated.
Journal of Physics Condensed Matter 07/2008; 20(27):275237. · 2.55 Impact Factor
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Sreedhar B. Dutta
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ABSTRACT: The kinetics of the long-range spherical model evolving from various initial states is studied. In particular, the large-time auto-correlation and -response functions are obtained, for classes of long-range correlated initial states, and for magnetized initial states. The ageing exponents can depend on certain qualitative features of initial states. We explicitly find the conditions for the system to cross over from ageing classes that depend on initial conditions to those that do not. Comment: 15 pages; corrected some typos
06/2008;
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Sreedhar B Dutta
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ABSTRACT: We study the large-time behavior of a class of periodically driven macroscopic systems. We find, for a certain range of the parameters of either the system or the driving fields, the time-averaged asymptotic behavior effectively is that of certain other equilibrium systems. We then illustrate with a few examples how the conventional knowledge of the equilibrium systems can be made use of in choosing the driving fields to engineer new phases and to induce new phase transitions.
Physical Review E 07/2004; 69(6 Pt 2):066115. · 2.26 Impact Factor
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ABSTRACT: We study the large-time behavior of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where these driving forces are rapidly oscillating with an amplitude that is not necessarily small. We develop a perturbative method for the high-frequency regime to find the large-time behavior of periodically driven stochastic systems. The asymptotic distribution of Brownian particles is then determined to second order. To first order, these particles are found to execute small-amplitude oscillations around an effective static potential that can have interesting forms.
Physical Review E 07/2003; 67(6 Pt 1):061111. · 2.26 Impact Factor
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ABSTRACT: We develop a systematic semiclassical approximation scheme for quantum Hall skyrmions near filling factors $\nu = {1 \over 2n+1}$, which is exact in the long wavelength limit. We construct a coherent state basis for the Hilbert space of Chern-Simons gauge fields and composite bosons with spin. These states are projected to the physical gauge invariant subspace and their wavefunctions explicitly evaluated. The lowest Landau level (LLL) condition is shown to be equivalent to an analyticity condition on the parameters. The matrix elements of physical observables between these states are shown to be calculable in the limit of small amplitude long wavelength density fluctuations. The electric charge density is shown to be proportional to the toplological charge density if and only if the LLL condition is satisfied. We then show that these states themselves form a generalised coherent state basis, parameterised by the values of physical observables. The theory can therefore be written in terms of these gauge invariant bosonic fields in the long wavelength regime. The off diagonal matrix elements of observables in these coherent states are computed and shown to vanish in the long wavelength limit. Thus we are able to prove that the classical description of the skyrmion is exact in the limit of large skyrmions.
08/2000;
