arXiv subjects

Smitarani Mishra

Publications and source records attributed to Smitarani Mishra.

3 recordsLinked to original sources

arXiv2025

Statistical entropy of quantum systems

Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical mechanics remain an area of active debate and are yet to be fully understood. This work is motivated by the need to develop a comprehensive understanding of the statistical measures of thermodynamic entropy in quantum systems - a topic intimately connected to the phenomenon of quantum thermalization. In particular, we investigate the conditions under which the von Neumann entropy can be regarded as a valid statistical measure of thermodynamic entropy in quantum systems. This paper demonstrates that the equivalence between the von Neumann and thermodynamic entropies is not universal, but instead depends on several subtle and often overlooked assumptions. In this context, we also briefly revisit key criticisms of von Neumann entropy - particularly its time-invariance and subadditivity - and argue that these concerns can be meaningfully addressed in the setting of thermodynamic systems. To substantiate some arguments and to clarify some issues, we provide suitable numerical results from our analysis of a spin-1/2 system.

quant-ph↗

arXiv2025

Quantum thermalization and average entropy of a subsystem

Page's seminal result on the average von Neumann (VN) entropy does not immediately apply to realistic many-body systems which are restricted to physically relevant smaller subspaces. We investigate here the VN entropy averaged over the pure states in the subspace $\mathcal{H}_E$ corresponding to a narrow energy shell centered at energy $E$. We find that the average entropy is $\overline{S}_{1} \simeq \ln d_1$, where $d_1$ represents first subsystem's effective number of states relevant to the energy scale $E$. If $d_E = \dim{(\mathcal{H}_E)}$ and $D$ ($D_1$) is the Hilbert space dimension of the full system (first subsystem), we estimate that $d_1 \simeq D_1^γ$, where $γ= \ln (d_E) / \ln (D)$ for nonintegrable (chaotic) systems and $γ< \ln (d_E) / \ln (D)$ for integrable systems. This result can be reinterpreted as a volume-law of entropy, where the volume-law coefficient depends on the density-of-states for nonintegrable systems, and remains below the maximal possible value for integrable systems. We numerically analyze a spin model to substantiate our main results.

quant-ph↗

arXiv2025

Quantum thermalization in a dimerized J1-J2 model

We revisit the J1-J2 frustrated Heisenberg spin-1/2 chain with dimerization (δ) or modulation in the nearest-neighbor couplings to investigate its thermalization behavior. While the dimerization tends to induce localization, the next-nearest-neighbor interaction J2 generally favors thermalization, making the assessment of the model's compliance with the Eigenstate Thermalization Hypothesis (ETH) particularly subtle. The challenge is further compounded by the model's SU(2) symmetry; the study of ETH compliance is necessarily done for each symmetry sector but separating different sectors of this symmetry is known to be a computationally demanding task. The current study is driven by two main motivations: first, to explore whether the well-known ground-state phases of the model have any bearing on its thermalization properties; and second, to understand how the interplay between two competing factors, namely, the non-uniformity (via δ) and the beyond-nearest-neighbor interactions (via J2) governs the system's approach to thermal equilibrium. A systematic analysis shows that the ETH is most strongly satisfied for intermediate values of δ (~ 0.5) with J2 ranging from intermediate (~ 0.5) to large (~ 1)- a parameter regime falls within the spiral ground-state phase. It is also found that when the system is in the gapless ground-state phase (which falls within the N'eel phase), the ETH is more prone to violation. In the regime of large δ and small J2, the system is seen to enter a localized phase (characterized here by modulation in density-of-states; assessing ETH compliance is less meaningful for this phase.

cond-mat.stat-mech↗