1,720,980 research outputs found
Accumulo e traslocazione di cromo trivalente nel pioppo (Populus x euramericana, clone I-214) allevato in substrati contaminati da reflui conciari
No full textDevelopment and chromium uptake in hybrid poplars cultivated on substrate polluted with industrial slags
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Violent relaxation in the Hamiltonian mean field model: II. Non-equilibrium phase diagrams
No full textA classical long-range-interacting N-particle system relaxes to thermal equilibrium on time scales growing with N; in the limit N → ∞ such a relaxation time diverges. However, a completely non-collisional relaxation process, known as violent relaxation, takes place on a much shorter time scale independent of N and brings the system towards a non-thermal quasi-stationary state (QSS). A finite system will eventually reach thermal equilibrium, while an infinite system will remain trapped in the QSS forever. For times smaller than the relaxation time, the distribution function of the system obeys the collisionless Boltzmann equation, also known as the Vlasov equation. The Vlasov dynamics are invariant under time reversal so that they do not 'naturally' describe the relaxational dynamics. However, as time grows the dynamics affect smaller and smaller scales in phase space, so that observables not depending upon small-scale details appear as relaxed after a short time. Herewith we present an approximation scheme able to describe violent relaxation in a one-dimensional toy-model, the Hamiltonian mean field. The approach described here generalizes the one proposed in Giachetti and Casetti (2019 J. Stat. Mech. 043201), which was limited to 'cold' initial conditions, to generic initial conditions, allowing us to predict non-equilibrium phase diagrams that turn out to be in good agreement with those obtained from the numerical integration of the Vlasov equation
Coarse-grained collisionless dynamics with long-range interactions
Full text linkWe present an effective evolution equation for a coarse-grained distribution function of a long-range-interacting system preserving the symplectic structure of the noncollisional Boltzmann, or Vlasov, equation. First, we derive a general form of such an equation based on symmetry considerations only. Then we explicitly derive the equation for one-dimensional systems, finding that it has the form predicted on general grounds. Finally, we use this equation to predict the dependence of the damping times on the coarse-graining scale and numerically check it for some one-dimensional models, including the Hamiltonian mean-field model, a scalar field with quartic interaction, a 1-d self-gravitating system, and a self-gravitating ring
Energy fluctuation relations and repeated quantum measurements
No full textIn this paper, we discuss the statistical description in non-equilibrium regimes of energy fluctuations originated by the interaction between a quantum system and a measurement apparatus applying a sequence of repeated quantum measurements. To properly quantify the information about energy fluctuations, both the exchanged heat probability density function and the corresponding characteristic function are derived and interpreted. Then, we discuss the conditions allowing for the validity of the fluctuation theorem in Jarzynski form 〈e−βQ〉=1, thus showing that the fluctuation relation is robust against the presence of randomness in the time intervals between measurements. Moreover, also the late-time, asymptotic properties of the heat characteristic function are analyzed, in the thermodynamic limit of many intermediate quantum measurements. In such a limit, the quantum system tends to the maximally mixed state (thus corresponding to a thermal state with infinite temperature) unless the system's Hamiltonian and the intermediate measurement observable share a common invariant subspace. Then, in this context, we also discuss how energy fluctuation relations change when the system operates in the quantum Zeno regime. Finally, the theoretical results are illustrated for the special cases of two- and three-levels quantum systems, now ubiquitous for quantum applications and technologies
Thermalization processes induced by quantum monitoring in multilevel systems
Full text linkWe study the heat statistics of a multilevel N-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number M of measurements (M→∞). In this context, the conditions allowing for an infinite-temperature thermalization (ITT), induced by the repeated monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the nonequilibrium evolution of the system and its initial state. Exceptions to ITT, which we refer to as partial thermalization, take place when the observable of the intermediate measurements is commuting (or quasicommuting) with the Hamiltonian of the quantum system or when the time interval between measurements is smaller or comparable with the system energy scale (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N→∞), describing continuous systems with a discrete spectrum, are also presented. We show that the order of the limits M→∞ and N→∞ matters: When N is fixed and M diverges, then ITT occurs. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A nontrivial result is obtained fixing M/N2 where instead partial ITT occurs. Finally, an example of partial thermalization applicable to rotating two-dimensional gases is presented
Berezinskii-Kosterlitz-Thouless Phase Transitions with Long-Range Couplings
Full text linkThe Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature TBKT. In this Letter, we consider the effect of long-range decaying couplings ∼r-2-σ on the BKT transition. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It features - for 7/4<σ<2 - a quasiordered phase in a finite temperature range TcTBKT. The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems
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