arXiv subjects

Amitabha Chakrabarti

Publications and source records attributed to Amitabha Chakrabarti.

8 recordsLinked to original sources

arXiv2026

Barrier crossing in a two-state system: Effect of bias and stochastic fields

We study barrier crossing in a two-state system, namely the kinetic Ising model, in the presence of a weak bias field and spatially homogeneous, but time-dependent, Gaussian random fields. We find that the bias field determines the location of the dominant maxima of the probability distribution function of the magnetization, whereas the noise intensity controls their sharpness and stability of the distribution. A moderate stochastic field lowers the effective energy barrier and facilitates transitions between ordered states, while strong noise induces broad distributions and significant backflow, which reduces directional selectivity. Our results suggest that efficient barrier crossing requires a balanced combination of moderate stochastic driving and controlled bias.

cond-mat.stat-mech↗

arXiv2026

Stochastic field effects in a two-state system: symmetry breaking and symmetry restoring

We study the Ising model under a time-varying, but spatially homogeneous, Gaussian random magnetic field. In the Monte Carlo simulations, we go beyond the standard analysis of the order parameter by measuring the magnetization probability distribution as a function of temperature and field strength, and by computing the time required for the system to escape from a completely ordered state of the magnetization. We identify three distinct phases: a soft-paramagnetic phase, a soft-ferromagnetic phase and a bona-fide ferromagnetic phase. These soft phases display broad magnetization distributions that tend to limiting forms that remain finite in both height and width in the thermodynamic limit. The transition between the soft-paramagnetic and soft-ferromagnetic phases is a noise-induced transition and, for small field amplitudes, occurs at the critical temperature of the field-free Ising model. The transition from the soft-ferromagnetic to the ferromagnetic phase occurs at lower temperatures and is discontinuous, yet it does not fall into the conventional first-order class. Instead, it is characterized by a diverging escape time from an ordered magnetization state.

cond-mat.stat-mech↗

arXiv2019

Effects of non-pairwise repulsion on nanoparticle assembly

Electrostatic interactions provide a convenient way to modulate interactions between nanoparticles, colloids, and biomolecules because they can be adjusted by the solution pH or salt concentration. While the presence of salt provides an easy method to control the net interparticle interaction, the nonlinearities arising from electrostatic screening make it difficult to quantify the strength of the interaction. In particular, when charged particles assemble into clusters or aggregates, nonlinear effects render the interactions strongly non-pairwise. Here we report Brownian dynamics simulations to investigate the effect that the non-pairwise nature of electrostatic interactions has on nanoparticle assembly. We compare these simulations to a system in which the electrostatics are modeled by a strictly pairwise Yukawa potential. We find that both systems show a narrow range in parameter space where the particles form well-ordered crystals. Bordering this range are regions where the net interactions are too weak to stabilize aggregated structures, or strong enough that the system becomes kinetically trapped in a gel. The non-pairwise potential differs from the pairwise system in the appearance of an amorphous phase for strongly charged particles. This phase appears because the many-body electrostatic interactions limit the maximum density achievable in an assembly.

cond-mat.soft↗

arXiv2012

New classes of spin chains from $(S\hat{O}_{(q)}(N)$, $S\hat{p}_{(q)}(N))$ Temperley-Lieb algebras: Data transmission and (q, N) parametrized entanglement entropies

A Temperley-Lieb algebra is extracted from the operator structure of a new class of $N^{2}\times N^{2}$ braid matrices presented and studied in previous papers and designated as $S\hat{O}_{(q)}(N)$, $S\hat{p}%_{(q)}(N)$ for the q-deformed orthogonal and symplectic cases respectively. Spin chain Hamiltonians are derived from such braid matrices and the corresponding chains are studied. Time evolutions of the chains and the possibility of transition of data encoded in the parameters of mixed states from one end to the other are analyzed. The entanglement entropies $% S(q,N)$ of eigenstates of the crucial operator, namely the q-dependent $% N^{2}\times N^{2}$ projector $P_{0}$ appearing in the corresponding Hamiltonian are obtained. Study of entanglements generated under the actions of \ $S\hat{O}(N)$, $S\hat{p}(N)$ braid operators, unitarized with imaginary rapidities is presented as a perspective.

math-ph↗

arXiv2010

Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity

We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological and quantum entanglement.

quant-ph↗

arXiv2010

Entangled three-particle states in magnetic field: Periodic correlations and density matrices

We present a novel study of the time evolutions of entangled states of three spin-1/2 particles in the presence of a constant external magnetic field, which causes the individual spins to precess and leads to remarkable periodicities in the correlations and density matrices. The emerging patterns of periodicity are studied explicitly for different entangled states and in detail for a particular initial configuration of the velocities. Contributions to precession of anomalous magnetic moments are analysed and general results are also obtained. We then introduce an electric field orthogonal to the magnetic field, linking to the preceding case via a suitable Lorentz transformation, and obtain the corresponding Wigner rotations of the spin states. Finally, we point out for the first time that the entangled states corresponding to well-known ones in the study of 3-particle entanglements, may be classified systematically using a particular coupling of three angular momenta.

quant-ph↗

arXiv1998

Phase Behavior of Binary Fluid Mixtures Confined in a Model Aerogel

It is found experimentally that the coexistence region of a vapor-liquid system or a binary mixture is substantially narrowed when the fluid is confined in a aerogel with a high degree of porosity (e.g. of the order of 95% to 99%). A Hamiltonian model for this system has recently been introduced (J.Donley PRE 55:539, 1997}. We have performed Monte-Carlo simulations for this model to obtain the phase diagram for the model. We use a periodic fractal structure constructed by diffusion-limited cluster-cluster aggregation (DLCA) method to simulate a realistic gel environment. The phase diagram obtained is qualitatively similar to that observed experimentally. We also have observed some metastable branches in the phase diagram which have not been seen in experiments yet. These branches, however, might be important in the context of recent theoretical predictions and other simulations.

cond-mat.stat-mech↗

arXiv1994

$SO(5)_{q}$ and Contraction

Representations of $SO(5)_{q}$ are constructed explicitly on the Chevalley basis for all $q$, generic and root of unity. Matrix elements of the generators are obtained for all representations depending on three variable indices, the maximal number being 4. A prescription for contraction is given such that a complete Hopf algebra is immediately obtained for the non-semisimple contracted case. For $q$ a root of unity the periodic representations for $SO(5)_{q}$ and the contracted algebra are obtained directly in the "fractional part" formalism which unifies the treatments for the generic and root of unity cases. The $q$-deformed quadratic Casimir operator is explicitly evaluated for the representations presented.

hep-th↗