The tight Second Law inequality for coherent quantum systems and finite-size heat baths

We propose a new form of the Second Law inequality that defines a tight bound for extractable work from the non-equilibrium quantum state. In classical thermodynamics, the optimal work is given by the difference of free energy, what according to the result of Skrzypczyk \emph{et al.} can be generalized for individual quantum systems. The saturation of this bound, however, requires an infinite bath and an ideal energy storage that is able to extract work from coherences. The new inequality, defined in terms of the ergotropy (rather than free energy), incorporates both of those important microscopic effects. In particular, we derive a formula for the locked energy in coherences, i.e. a quantum contribution that cannot be extracted as a work, and we find out its thermodynamic limit. Furthermore, we establish a general relation between ergotropy and free energy of the arbitrary quantum system coupled to the heat bath, what reveals that the latter is indeed the ultimate thermodynamic bound regarding work extraction, and shows that ergotropy can be interpreted as the generalization of the free energy for the finite-size heat baths

Work distributions for random sudden quantum quenches

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of hermitean matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature

Łamanie nierówności Leggetta-Garga w otwartych układach kwantowych

Pełny tekst artykułu nr 3, dołączonego do rozprawy, dostępny jest lokalnie w sieci bibliotek Uniwersytetu Śląskiego: http://www.bc.us.edu.pl/publication/16367This dissertation concerns an analysis of obtained theoretical values of temporal correlation functions in open quantum systems in the context of Leggett-Garg inequalities. The violation of these inequalities indicates that a system reveals non-classical correlations. A special case of the temporal correlations, analysed in this work, are used to tests of macrorealism, likewise as an indicator of the “quantumness” of a system or in order to perform the quantum information protocols. Despite of the well grounded results on the temporal quantum correlations in isolated systems, the open systems are still barely explored. The main motivation to study this subject is a possibility to obtain better models of real physical systems and to develop new methods to control the amount of the non-classical correlations. The main research objective is to establish an influence on the amount of the non-classical correlations in the measured subsystem by a coupling with the environment. In this work, four distinct physical models of open quantum systems are presented. In the first one there is revealed a violation of Leggett-Garg inequality in the system weakly coupled to thermal environment where especially is discussed the process of decoherence and dissipation. The main result is an observation that, under some conditions, the violation of the inequality is independent of environment properties like temperature. The second model concerns an analysis of temporal quantum correlations in the systems that dynamics is governed by the angular momentum operators and driven by classical white noise. In this case strict analytical results reveal an exponential dumping of the non-classical correlations as well as a property that such dumping can be less effective for systems with larger state space. The last but not least two models for which is calculated the Leggett-Garg correlator are the systems which interact with the environment due to the spin-spin coupling. In this context, a physical model of atoms from the first group of the periodic table and a model of quantum-classical hybrids, for which is discussed the semi-classical approach, is proposed. In both examples it is proven that for “more macroscopic” systems as well as for “classical environments”, it is possible to observe higher violation of the Leggett-Garg inequality

Violation of Leggett-Garg inequalities for quantum-classical hybrids

Violation of Leggett{Garg inequalities can serve as a signature of a failure of (macroscopic) realism. We investigate violation of the simplest Leggett{Garg inequality for a qubit coupled to an integer j spin (angular momentum). Such a system e ectively reveals quantum{classical hybrid behavior in the limit of large j values. We show that a maximal violation of the Leggett{ Garg inequality is larger for quantum{classical hybrids than for fully quantum systems

Quantum contextuality of a single neutrino under interactions with matter

We study contextuality of the three neutrinos oscillations using the Klyachko-Can-Binicioglu-Shumovsky 5-observable test. We show how the interaction between neutrinos and normal matter affects contextuality - its loss and its possible revivals. We show that for open neutrino's system, interacting with an environment, revivals of contextuality survive in a presence of decoherence included in the neutrino's Lindblad-Kossakowski master equation in a simplest Markovian approximatio

Leggett–Garg inequalities for a quantum top affected by classical noise

The violation of the Leggett–Garg inequality is studied for a quantum top (with angular momentum Jz of integer or half-integer size), being driven by classical Gaussian white noise. The form of a longitudinal (Jz) or a transverse (Jx ) coupling of noise to the angular momentum affects both (i) to what extent the Leggett–Garg inequality is violated and (ii) how this violation is influenced by the size j of the spinning top and direction of a coupling (transverse or longitudinal).We introduce j - independent method, using two- dimensional invariant subspace of the system Hilbert space, which allows us to find out strict analytical solution for a noise-free system and with longitudinal coupling and to extract from the whole dynamics effects purely induced by a noise. It is demonstrated that in the semi-classical limit of a large angular momentum j and for the transverse coupling, the Leggett–Garg inequalities become more strongly violated as compared to the deep quantum regime of small j

Payoffs and coherence of a quantum two-player game in a thermal environment

A two-player quantum game is considered in the presence of a thermal decoherence modeled in terms of a rigorous Davies approach. It is shown how the energy dissipation and pure decoherence affect the payoffs of the players of the (quantum version) of prisoner dilemma. The impact of the thermal environment on a coherence of game, as a quantum system, is also presented

Quantum two player game in thermal environment

A two-player quantum game is considered in the presence of thermal decoherence. It is shown how the thermal environment modeled in terms of rigorous Davies approach affects payoffs of the players. The conditions for either beneficial or pernicious effect of decoherence are identified. The general considerations are exemplified by the quantum version of Prisoner Dilemm