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We study phase transitions in $SU(\infty)$ gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the…
We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary…
Finding microscopic models for metallic states that exhibit quantum critical properties such as $\omega/T$ scaling is a major theoretical challenge. We calculate the local dynamical spin susceptibility $\chi(T,\omega)$ for a Hubbard model…
Quantum thermodynamics studies quantum effects in thermal machines. But when is a heat engine, which cyclically interacts with external reservoirs that unavoidably destroy its quantum coherence, really quantum? We here use the Leggett-Garg…
Quantum thermal machines make use of non-classical thermodynamic resources, one of which is interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based…
We study the quantum fidelity approach to characterize thermal phase transitions. Specifically, we focus on the mixed-state fidelity induced by a perturbation in temperature. We consider the behavior of fidelity in two types of second-order…
We study internal work optimization over the energy levels of a generic hot quantum Otto engine. We find universal features in the efficiency that resembles the classical external power optimization over the coupling times to the thermal…
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding…
We derive the probability distribution of the efficiency of a quantum Otto engine. We explicitly compute the quantum efficiency statistics for an analytically solvable two-level engine. We analyze the occurrence of values of the stochastic…
Quantum phase transitions (QPTs) in the spin-boson model with/without the rotating-wave approximation (RWA) are systematically investigated through variational calculations using a sub-Ohmic bath with high spectral density. Four cases…
The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function…
A procedure is proposed to study QFT at zero or at finite temperature by a sequence of real space renormalization group (RG) or blockspin transformations. They transform to effective theories on coarser and coarser lattices.The ultimate aim…
We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
We derive the general probability distribution function of stochastic work for quantum Otto engines in which both the isochoric and driving processes are irreversible due to finite time duration. The time-dependent power fluctuations,…
Thermal operations are an operational model of non-equilibrium quantum thermodynamics. In the absence of coherence between energy levels, exact state transition conditions under thermal operations are known in terms of a mathematical…
Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the…
Quantum phase transitions occur at zero temperature when some non-thermal control-parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a…
We study three regimes of the Mott transitions characterized by classical, marginally quantum and quantum. In the classical regime, the quantum degeneracy temperature is lower than the critical temperature of the Mott transition, Tc, below…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…