arXiv subjects

Oskar A. Prośniak

Publications and source records attributed to Oskar A. Prośniak.

7 recordsLinked to original sources

arXiv2026

Star Topology Optimizes the Charging Power of Quantum Batteries

Quantum batteries are quantum systems that store energy and deliver it on demand, and their practical value hinges on how fast they can be charged. While collective charging protocols and global control are known to enhance charging power, it remains unclear how the battery's internal interaction architecture itself constrains performance. Here we study interacting fermionic batteries whose internal couplings are encoded by a graph adjacency matrix, charged via a simple interaction with an external fermionic device. We prove that the star topology maximises the early time charging power, which proxies the maximal average power - a widely used quantum battery quality metric. We substantiate the result numerically by an exhaustive sweep over all graphs with $N\leq 7$ vertices and by benchmarks against random graph ensembles at larger $N$. Our findings shed light on architecture as a controllable knob for fast charging and motivate hub-and-spoke designs in scalable quantum-battery platforms.

quant-ph↗

arXiv2025

A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators

Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and incoherent directions and provide their physical interpretation. This understanding enables us to optimize the success rate of non-Hermitian driving along prescribed trajectories, with direct relevance to shortcuts to adiabaticity. Next, we explore the geometric interpretation of a speed limit for non-Hermitian Hamiltonians and analyze its tightness. We derive the explicit expression that saturates this bound and illustrate our results with a minimal example of a dissipative qubit.

quant-ph↗

arXiv2025

Long persistence of localization in a disordered anharmonic chain beyond the atomic limit

We establish rigorous bounds on the decorrelation time and thermal transport in the disordered Klein-Gordon chain with a quartic on-site potential, governed by a parameter $λ$. At $λ= 0$, the chain is harmonic, and any form of transport is fully suppressed by Anderson localization. For the anharmonic system, at $λ> 0$, our results show that decorrelation and transport can occur only on time scales that grow faster than any polynomial in $1/λ$ as $λ\to 0$. From a technical perspective, the main novelty of our work is that we don't restrict ourselves to the atomic limit. Instead, we develop perturbation theory around the harmonic system with a fixed harmonic interaction between nearby oscillators. This allows us to compare our mathematical results with previous numerical work and contribute to resolving an ongoing debate, as detailed in a companion paper arXiv:2308.10572.

math-ph↗

arXiv2025

Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds

We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter $λ$, and on the other hand our numerics show that it follows a power law for a broad range of values of $λ$. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems.

cond-mat.stat-mech↗

arXiv2023

Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain

This paper originates from lectures delivered at the summer school "Fundamental Problems in Statistical Physics XV" in Bruneck, Italy, in 2021. We give a brief and limited introduction into ergodicity-breaking induced by disorder. As the title suggests, we include a simple yet rigorous and original result: For a strongly disordered quantum chain, we exhibit a full set of quasi-local quantities whose dynamics is negligible up to times of order $\exp\{ c (\log W)^{2-ε}\}$, with $ε< 1$, $c$ a numerical constant, and $W$ the disorder strength. Such a result, that is often referred to as "quasi-localization", can in principle be obtained in other systems as well, but for a disordered quantum chain, its proof is relatively short and transparent.

math-ph↗

arXiv2019

Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations

We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.

cond-mat.quant-gas↗

arXiv2018

Quantum critical point of the Ising chain from boundary effects

We propose two easy-to-study observables in the quantum Ising chain with open boundary conditions. They measure the length at which boundaries affect the longitudinal or transverse magnetization. We show that their finite-size scaling behaviour encodes the position of the quantum critical point and the universal scaling exponent $ν$. The applicability of proposed observables in small systems is also discussed. We expect that our results will be useful in quantum simulation of spin systems.

cond-mat.stat-mech↗