arXiv subjects

Shimul Akhanjee

Publications and source records attributed to Shimul Akhanjee.

14 recordsLinked to original sources

arXiv2026

The Statistical Mechanics of Indistinguishable Energy States and the Glass Transition

The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy, the energy sub-levels or sub-states are universally treated as distinguishable, and differentiated by unique quantum numbers, or addressed by distinct spatial locations. Results from combinatorial counting problems are adapted to derive exact distribution functions for both classical and quantum particles at a high degeneracy limit. Quantum particles obey a non-extensive entropy $\mathcal{S} \propto \sqrt{N}$, that satisfies an Area Law: $\mathcal{S}\propto A$ in $d=2$ bulk spatial dimensions. Classical particles exhibit a definitive glass transition, similar to supercooled liquids where the configurational entropy vanishes below a finite temperature $T_K$.

cond-mat.stat-mech↗

arXiv2024

Distribution Function for $n \ge g$ Quantum Particles

A new quantum mechanical distribution function $n^I(\varepsilon)$, is derived for the condition $n \ge g$, where in contrast to the exclusion principle $n \le g$ for fermions, each energy state must be populated by at least one particle. Although the particles share many features with bosons, the anomalous behavior of $n^I(\varepsilon)$ precludes Bose-Einstein condensation (BEC) due to the required occupancy of the excited states, which creates a permanently pressurized background at $T=0$, similar to the degeneracy pressure of fermions. An exhaustive classification scheme is presented for both distinguishable and indistinguishable, particles and energy levels based on Richard Stanley's twelvefold way in combinatorics.

cond-mat.quant-gas↗

arXiv2013

Composite pairing and superfluidity in a one-dimensional resonant Bose-Fermi mixture

We study the ground-state properties of one-dimensional mixtures of bosonic and fermionic atoms resonantly coupled to fermionic Feshbach molecules. When the particle densities of fermionic atoms and Feshbach molecules differ, the system undergoes various depletion transitions between binary and ternary mixtures, as a function of the detuning parameter. However, when the particle densities of fermionic atoms and Feshbach molecules are identical, the molecular conversion and disassociation processes induce a gap in a sector of low-energy excitations, and the remaining system can be described by a two-component Tomonaga-Luttinger liquid. Using a bosonization scheme, we derive the effective low-energy Hamiltonian for the system, which has a similar form as that of the two-chain problem of coupled Tomonaga-Luttinger liquids. With the help of improved perturbative renormalization group analysis of the latter problem, we determine the ground-state phase diagram and find that it contains a phase dominated by composite superfluid or pairing correlations between the open and closed resonant channels.

cond-mat.quant-gas↗

arXiv2012

Non-perturbative Solution of the Unitary, $N$-Orbital Anderson Model

The mobility edge is extracted from a non-perturbative analysis of F. Wegner's real matrix ensemble (RME), $N$-orbital model of electrons with broken time-reversal invariance moving in random potential. The replicon fluctuations around the zero-dimensional (0D), single metallic grain saddlepoint, are shown to destabilize diffusive regime beyond the low energy limit yielding a precise criteria of localization in terms of a single scaling parameter.

cond-mat.dis-nn↗

arXiv2010

Quasiparticle excitations in Bose-Fermi mixtures

We analyze the excitation spectrum of a three-dimensional(3D) Bose-Fermi mixture with tunable resonant interaction parameters and high hyperfine spin multiplets. We focus on a 3-particle vertex describing fermionic and bosonic atoms which can scatter to create fermionic molecules or disassociate. For a single molecular level, in analogy to the single magnetic impurity problem we argue that the low lying excitations of the mean-field theory are described by the Fermi liquid picture with a quasiparticle weight and charge which is justified by a $1/N_ψ$ expansion, expected to be exact in the limit of infinite degeneracy (or very high fermionic spin) $N_ψ\to \infty$. Our emphasis is placed on the novel conditions for chemical equilibrium and how many-body chemical reactions renormalize the bosonic chemical potential, modifying condensation and superfluid-insulator transitions.

cond-mat.quant-gas↗

arXiv2010

Quantum phase coherence in non-Markovian and reaction-diffusive transport

We study quantum phase coherence and weak localization (WL) in disordered metals with restricted back-scattering and phenomenologically formulate a large class of unconventional transport mechanisms as modified diffusion processes not captured by the Boltzmann picture. Inspired by conductivity measurements in ferromagnetic films and semiconductors where anomalous power law corrections have been observed, we constrain memory dependent, self avoidance effects onto the quantum enhanced back-scattered trajectories, drastically altering the effect of weak localization in two dimensions (2D). Scale dependent corrections to the conductivity fail to localize the electrons in $d \ge 2$ for sufficiently weak disorder. Additionally, we analyze quantum transport in reaction-diffusion systems governed by the Fisher's equation and observe asymptotically similar delocalization in 2D. Such unconventional transport might be relevant to certain non-Fermi liquid or strongly correlated phases in 2D within the negative compressibility regime.

cond-mat.dis-nn↗

arXiv2010

Spherical spin-glass - Coulomb gas duality: solution beyond mean-field theory

We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé $τ^{IV} [n]$ function in the $n\to 0$ limit. The large $N$ thermodynamics exactly recovers that of Kosterlitz, Thouless and Jones \cite{ktjonesPRL}. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.

cond-mat.dis-nn↗

arXiv2009

Spin-selective localization due to intrinsic spin-orbit coupling

We study spin-dependent diffusive transport in the presence of a tunable spin-orbit (SO) interaction in a two-dimensional electron system. The spin precession of an electron in the SO coupling field is expressed in terms of a covariant curvature, affecting the quantum interference between different electronic trajectories. Controlling this curvature field by modulating the SO coupling strength and its gradients by, e.g., electric or elastic means, opens intriguing possibilities for exploring spin-selective localization physics. In particular, applying a weak magnetic field allows the control of the electron localization independently for two spin directions, with the spin-quantization axis that could be "engineered" by appropriate SO interaction gradients.

cond-mat.mes-hall↗

arXiv2009

Negative effective mass transition and anomalous transport in power-law hopping bands

We study the stability of spinless Fermions with power law hopping $H_{ij} \propto |i - j|^{-α}$. It is shown that at precisely $α_c =2$, the dispersive inflection point coalesces with the band minimum and the charge carriers exhibit a transition into negative effective mass regime, $m_α^* < 0$ characterized by retarded transport in the presence of an electric field. Moreover, bands with $α< 2$ must be accompanied by counter-carriers with $m_α^* > 0$, having a positive band curvature, thus stabilizing the system in order to maintain equilibrium conditions and a proper electrical response. We further examine the semi-classical transport and response properties, finding an infrared divergent conductivity for 1/r hopping($α=1$). The analysis is generalized to regular lattices in dimensions $d$ = 1, 2, and 3.

cond-mat.mes-hall↗

arXiv2008

Perturbative criteria for Anderson localization in long-ranged 1D tight-binding models

We develop an alternative scaling approach to determine the criteria for Anderson localization in one-dimensional tight-binding models with random site energies having a bandwidth that decays as a power law in space, $H_{ij} \propto |i - j|^{-α}$. At the first order in perturbation theory the scale dependence of the exchange-narrowed energy of the disorder is compared to the energy level spacing of the ideal system to establish whether or not the disorder has a perturbative effect on the Bloch states. We find that at $α=1$, the perturbative condition is satisfied and for sufficiently weak disorder strength all states are extended. For $α> 1$, all states are localized for arbitrary disorder strength, in agreement with the earlier renormalization group treatment by Levitov.

cond-mat.dis-nn↗

arXiv2008

Spin-charge separation in a strongly correlated spin-polarized chain

We combine the first-quantized path-integral formalism and bosonization to develop a phenomenological theory for spin-charge coupled dynamics in one-dimensional (1D) ferromagnetic systems with strong interparticle repulsion, at low temperatures. We assume an effective spin-charge separation and retain the standard Luttinger-liquid plasmon branch, which is explicitly coupled to a ferromagnetic spin-wave texture with a quadratic dispersion. The dynamic spin structure severely suppresses the plasmon peak in the single-particle propagator, in both fermionic and bosonic systems. Our analysis provides an effective theory for the new universality class of 1D ferromagnetic systems, capturing both the trapped spin and propagating spin-wave regimes of the long-time behavior.

cond-mat.str-el↗

arXiv2008

Anderson transition of the plasma oscillations of 1D disordered Wigner lattices

We report the existence of a localization-delocalization transition in the classical plasma modes of a one dimensional Wigner Crystal with a white noise potential environment at T=0. Finite size scaling analysis reveals a divergence of the localization length at a critical eigenfrequency. Further scaling analysis indicates power law behavior of the critical frequency in terms of the relative interaction strength of the charges. A heuristic argument for this scaling behavior is consistent with the numerical results. Additionally, we explore a particular realization of random-bond disorder in a one dimensional Wigner lattice in which all of the collective modes are observed to be localized.

cond-mat.dis-nn↗

arXiv2008

Disorder induced transition into a one-dimensional Wigner glass

The destruction of quasi-long range crystalline order as a consequence of strong disorder effects is shown to accompany the strict localization of all classical plasma modes of one-dimensional Wigner crystals at T=0. We construct a phase diagram that relates the structural phase properties of Wigner crystals to a plasmon delocalization transition recently reported. Deep inside the strictly localized phase of the strong disorder regime, we observe ``glass-like'' behavior. However, well into the critical phase with a plasmon mobility edge, the system retains its crystalline composition. We predict that a transition between the two phases occurs at a critical value of the relative disorder strength. This transition has an experimental signature in the AC conductivity as a local maximum of the largest spectral amplitude as a function of the relative disorder strength.

cond-mat.dis-nn↗

arXiv2007

Exact longitudinal plasmon dispersion relations for one and two dimensional Wigner crystals

We derive the exact longitudinal plasmon dispersion relations, $ω(k)$ of classical one and two dimensional Wigner crystals at T=0 from the real space equations of motion, of which properly accounts for the full unscreened Coulomb interactions. We make use of the polylogarithm function in order to evaluate the infinite lattice sums of the electrostatic force constants. From our exact results we recover the correct long-wavelength behavior of previous approximate methods. In 1D, $ω(k) \sim | k |\log ^{1/2} (1/k)$, validating the known RPA and bosonization form. In 2D $ω(k) \sim \sqrt k$, agreeing remarkably with the celebrated Ewald summation result. Additionally, we extend this analysis to calculate the band structure of tight-binding models of non-interacting electrons with arbitrary power law hopping.

cond-mat.str-el↗