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Periodically driven thermodynamic systems support stable non-equilibrium oscillating states with properties drastically different from equilibrium. They exhibit even more exotic features for low viscous drives, which is a regime that is hard to probe due to singular behavior of the underlying Langevin dynamics near vanishing viscosity. We propose a method, based on singular perturbation and Floquet theories, that allows us to obtain oscillating states in this limit. We then find two distinct classes of distributions, each exhibiting interesting features that can be exploited for a range of practical applicability, including cooling a system and triggering chemical reactions through weakly interacting driven environments., Comment: 6+13 pages, 2+4 figures

We employ an appropriate perturbative scheme in the large viscous regime to study oscillating states in driven Langevin systems. We explicitly determine oscillating state distribution of under-damped Brownian particle subjected to thermal, viscous and potential drives to linear order in anharmonic perturbation. We also evaluate various non-equilibrium observables relevant to characterize the oscillating states. We find that the effects of viscous drive on oscillating states are measurable even in the leading order and show that the thermodynamic properties of the system in these states are immensely distinct from those in equilibrium., Comment: 14 pages, 2 figures

We investigate the asymptotic distributions of periodically driven anharmonic Langevin systems. Utilizing the underlying $SL_2$ symmetry of the Langevin dynamics, we develop a perturbative scheme in which the effect of periodic driving can be treated nonperturbatively to any order of perturbation in anharmonicity. We spell out the conditions under which the asymptotic distributions exist and are periodic, and show that the distributions can be determined exactly in terms of the solutions of the associated Hill equations. We further find that the oscillating states of these driven systems are stable against anharmonic perturbations., Comment: 11 pages, 2 figures

Motivated to understand the asymptotic behavior of periodically driven thermodynamic systems, we study the prototypical example of Brownian particle, overdamped and underdamped, in harmonic potentials subjected to periodic driving. The harmonic strength and the coefficients of drift and diffusion are all taken to be $T$-periodic. We obtain the asymptotic distributions almost exactly treating driving nonperturbatively. In the underdamped case, we exploit the underlying $SL_2$ symmetry to obtain the asymptotic state, and study the dynamics and fluctuations of energies and entropy. We further obtain the two-time correlation functions, and investigate the responses to drift and diffusion perturbations in the presence of driving., Comment: Journal version; added comments on nonperturbative treatment and the advantages of the method used, including an illustrative example; removed an erroneous statement and related comments that has no bearing on any equation

We analyse the spin-flip dynamics in kinetic Ising chains with Kimball-Deker-Haake (KDH) transition rates, and evaluate exactly the evolution of global quantities like magnetisation and its fluctuations, and the two-time susceptibilities and correlations of the global spin and the global three-spin. Information on the ageing behaviour after a quench to zero temperature is extracted.

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., Comment: Included RG analysis and discussion on new universality classes

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

The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance., Comment: added "fluctuation-dissipation ratios"; fixed typos

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 in choosing the driving fields to engineer new phases and to induce new phase transitions., Comment: LaTex, 8 pages

We study the large-time behaviour 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 which can have interesting forms., Comment: 8 pages; Included an e.g. in the last section; added references; final version in two columns

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., Comment: 28 pages, latex file