arXiv subjects

Sina Kazemian

Publications and source records attributed to Sina Kazemian.

8 recordsLinked to original sources

arXiv2026

Biorthogonal Time-Dependent Variational Principle for Non-Hermitian Systems

We develop a biorthogonal time-dependent variational principle for real-time dynamics of non-Hermitian quantum many-body systems. Independent left and right matrix-product states obey coupled bivariational tangent-space equations whose cross-Gram matrix defines an oblique projection. A matrix-free scaled Taylor action propagates the resulting non-normal local generators without assembling dense matrices or storing a Krylov basis. We distinguish the fully coupled algorithm, which solves the cross-pairing problem and truncates the two bond bases jointly, from an efficient independently propagated approximation used for large systems. Independent truncation can make the retained left-right pairing nearly singular; overlap drift and the smallest singular value of the bond cross matrix expose this failure, while coupled truncation substantially delays it. Exact benchmarks and convergence tests validate the method. Applied to an interacting long-range non-Hermitian Ising chain, it resolves a biorthogonal dynamical quantum phase transition and shows that a weak imaginary field shifts the leading critical time from $t^{\ast}|J|=1.84$ to $1.04$.

quant-ph↗

arXiv2026

Closed Quantum Boltzmann Bridges: Coherent Revivals, Hidden Microstates, and the Emergence of Classical Two-Time Entropy Conditioning

The classical Boltzmann Bridge describes entropy histories conditioned on both an initial low-entropy macrostate and a later macrostate. Unlike the usual past-only formulation of the thermodynamic arrow, this two-time conditioning can produce entropy profiles that rise above the final entropy and then decrease toward the imposed endpoint. In this work, we formulate closed quantum analogues of the Boltzmann Bridge using macro-subspace projectors, unitary time evolution, and Boltzmann entropy defined by the dimension of coarse-grained macroscopic sectors. We first study a minimal coherent chamber-qubit model, in which each particle has only a two-state chamber degree of freedom. Although this model is the most direct quantization of the classical two-box system, its bridge entropy profile is dominated by coherent oscillations and revivals rather than classical relaxation. We then introduce a hidden-microstate bridge, in which each chamber sector contains unresolved internal degrees of freedom while the full dynamics remain unitary. Numerical experiments show that increasing the internal Hilbert-space dimension suppresses sample-dependent revival behavior and produces bridge entropy profiles whose sign structure and coarse-grained shape increasingly agree with the classical Boltzmann Bridge. We further use a Random Forest classifier to explore the parameter regime separating revival-dominated quantum behavior from classical-like coarse-grained bridge behavior. These results suggest that classical two-time-conditioned entropy behavior is not recovered by quantizing the chamber variable alone, but can emerge statistically from closed quantum.

quant-ph↗

arXiv2026

Boundary-Aware QFT Block-Encoding of Fractional Laplacians

We study the quantum Fourier transform (QFT) block-encoding of the semi-discrete fractional Laplacian on bounded domains with open, zero-extension boundary conditions. In the notation of the main construction, the target operator is the finite Toeplitz truncation $A^{(N)}_{α,h}$ obtained from the full-lattice semi-discrete operator with symbol $|ξ|^α$. A finite QFT register, however, diagonalizes circulant matrices rather than Toeplitz truncations. The native QFT circuit therefore implements a periodic surrogate $\widetilde A^{(N)}_{α,h}$, not the open-boundary operator. We identify this mismatch through an exact Toeplitz-to-circulant aliasing identity. To recover the open-boundary action, we zero-pad the state into a larger $M$-point QFT register, apply the same Fourier-symbol block-encoding, and compress back to the physical subspace. The resulting compressed block satisfies $P_{N\to M}^{\dagger}\widetilde A^{(M)}_{α,h}P_{N\to M} = A^{(N)}_{α,h}+E^{(M)}$, where $E^{(M)}$ is controlled by the tail of the semi-discrete convolution kernel. Thus, the QFT layer implements the fractional symbol, while zero-padding supplies the open-boundary geometry. The construction is an operator-compilation primitive for boundary-aware quantum simulation rather than a complete PDE solver.

quant-ph↗

arXiv2025

Electron-Phonon interaction and lattice thermal conductivity from metals to 2D Dirac crystals: a review

Electron--phonon (e--ph) coupling governs electrical resistivity, hot-carrier cooling, and critically, thermal transport in solids. Recent first-principles advances now predict e--ph limited thermal conductivity from d-band metals and wide-band-gap semiconductors to 2D Dirac crystals without empirical parameters. In bulk metals, ab-initio lifetimes show that phonons, though secondary, still carry up to 40\% of the heat once e--ph scattering is included. We next survey coupled Boltzmann frameworks, exemplified by \textsc{elphbolt}, that capture mutual drag and ultrafast non-equilibrium in semiconductors. For 2D Dirac crystals, mirror symmetry, carrier density, strain, and finite size rearrange the scattering hierarchy: ZA modes dominate pristine graphene yet become the main resistive branch in nanoribbons once symmetry is broken. At low Fermi energies and high temperatures, the standard 3-particle decay is partially cancelled, elevating 4-particle processes and necessitating dynamically screened, higher-order theory. Throughout, we identify the microscopic levers such as the electronic density of states, phonon frequency, deformation potential, and show how doping, strain, or dielectric environment can tune e--ph damping. We conclude by outlining open challenges such as: developing coupled e--ph solvers, solving the full mode-to-mode Peierls--Boltzmann equation with 4-particle terms, embedding correlated electron methods in e--ph workflows, and leveraging higher-order e--ph coupling and symmetry breaking to realise phononic thermal diodes and rectifiers. Solving these challenges will elevate e--ph theory from a diagnostic tool to a predictive, parameter-free platform that links symmetry, screening, and many-body effects to heat and charge transport in next-generation electronic, photonic, and thermoelectric devices.

cond-mat.mtrl-sci↗

arXiv2025

An uncertainty-aware physics-informed neural network solution for the Black-Scholes equation: a novel framework for option pricing

We present an uncertainty-aware, physics-informed neural network (PINN) for option pricing that solves the Black--Scholes (BS) partial differential equation (PDE) as a mesh-free, global surrogate over $(S,t)$. The model embeds the BS operator and boundary/terminal conditions in a residual-based objective and requires no labeled prices. For American options, early exercise is handled via an obstacle-style relaxation while retaining the BS residual in the continuation region. To quantify \emph{epistemic} uncertainty, we introduce an anchored-ensemble fine-tuning stage (AT--PINN) that regularizes each model toward a sampled anchor and yields prediction bands alongside point estimates. On European calls/puts, the approach attains low errors (e.g., MAE $\sim 5\times10^{-2}$, RMSE $\sim 7\times10^{-2}$, explained variance $\approx 0.999$ in representative settings) and tracks ground truth closely across strikes and maturities. For American puts, the method remains accurate (MAE/RMSE on the order of $10^{-1}$ with EV $\approx 0.999$) and does not exhibit the error accumulation associated with time-marching schemes. Against data-driven baselines (ANN, RNN) and a Kolmogorov--Arnold FINN variant (KAN), our PINN matches or outperforms on accuracy while training more stably; anchored ensembles provide uncertainty bands that align with observed error scales. We discuss design choices (loss balancing, sampling near the payoff kink), limitations, and extensions to higher-dimensional BS settings and alternative dynamics.

q-fin.CP↗

arXiv2024

Influence of higher order electron-phonon interaction on the electron-related lattice thermal properties of 2d Dirac crystal

To understand the essential properties of Dirac crystals, such as their thermal conductivity, we require models that consider the interaction between Dirac electrons and dispersive acoustic phonons. The exceptionally high thermal conductivity in 2D Dirac crystals is attributed to near-ideal phonon quantum gases, while undesired limitations arise from electron-phonon (e-ph) interactions which have been shown to limit the thermal conductivity up to several microns away. The e-ph thermal conductivity is directly linked to the phonon scattering rate. Conventional calculations overlook phonons with short-dispersive wavelengths, rendering them inadequate for analyzing 2D Dirac crystals. The phonon scattering rate is typically calculated up to the first-order magnitude, considering 3-particle interactions involving the decay of an electron and phonon (EP-E*) to create a new electron. However, processes involving the decay of an electron and the creation of a new electron and phonon (E-E*P*) are neglected. In this study, we present an accurate expression for the phonon scattering rate and e-ph thermal conductivity in 2D Dirac crystals, accounting for short-dispersive wavelength phonons. We demonstrate the significance of the E-E*P* process even at room temperature in calculating the phonon scattering rate and e-ph thermal conductivity, particularly for first-order e-ph interactions. Furthermore, we emphasize the importance of incorporating second-order e-ph interactions, specifically the EP-E*P* interaction involving the decay of an electron and phonon and the creation of a new electron-phonon pair, to accurately determine the phonon scattering rate and e-ph thermal conductivity at high temperatures and low Fermi energies. This 4-particle interaction process plays a crucial role in characterizing these properties effectively.

cond-mat.mes-hall↗

arXiv2023

Diffuse emission from black hole remnants

We point out that conservation of information implies that remnants produced at the end of black hole evaporation should radiate in the low-frequency spectrum. We model this emission and derive properties of the diffuse radiation emitted by an otherwise dark population of such objects. We show that for early universe black holes the frequency and energy density of this radiation, which are in principle measurable, suffice to estimate the remnant density.

gr-qc↗

arXiv2023

Dynamic dielectric function and phonon self-energy from electrons strongly correlated with acoustic phonons in 2D Dirac crystals

The unique structure of two-dimensional (2D) Dirac crystals, with electronic bands linear in the proximity of the Brillouin-zone boundary and the Fermi energy, creates anomalous situations where small Fermi-energy perturbations are known to critically affect the electron-related lattice properties of the system. The Fermi-surface nesting (FSN) conditions determining such effects via electron-phonon interaction, require accurate estimates of the crystal's response function $(χ)$ as a function of the phonon wavevector q for any values of temperature. Numerous analytical estimates of $χ(q)$ for 2D Dirac crystals beyond the Thomas-Fermi approximation have been so far carried out only in terms of dielectric response function $χ(q,ω)$, for photon and optical-phonon perturbations, due to relative ease of incorporating a q-independent oscillation frequency in their calculation. However, models accounting for Dirac-electron interaction with ever-existing acoustic phonons, for which $ω$ does depend on q and is therefore dispersive, are essential to understand many critical crystal properties. The lack of such models has often led to assume that the dielectric response function $χ(q)$ in these systems can be understood from free-electron behavior. Here, we show that, different from free-electron systems, $χ(q)$ calculated from acoustic phonons in 2D Dirac crystals using the Lindhard model, exhibits a cuspidal point at the FSN condition. Strong variability of $\frac{\partialχ}{\partial q}$ persists also at finite temperatures, while $χ(q)$ may tend to infinity in the dynamic case even where the speed of sound is small, albeit nonnegligible, over the Dirac-electron Fermi velocity. The implications of our findings for electron-acoustic phonon interaction and transport properties such as the phonon line width derived from the phonon self energy will also be discussed.

cond-mat.mes-hall↗