arXiv subjects
Publications and source records attributed to Giuliano Benenti.
We show that generic systems with a single relevant conserved quantity reach the Carnot efficiency in the thermodynamic limit. Such a general result is illustrated by means of a diatomic chain of hard-point elastically colliding particles where the total momentum is the only relevant conserved quantity.
We show that for quantum phase transitions with a single bosonic zero mode at the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model, metric quantities such as fidelity, that is, the overlap between two ground states corresponding to two values $λ_1$ and $λ_2$ of the controlling parameter $λ$, only depend on the ratio $η=(λ_1-λ_c)/(λ_2-λ_c)$, where $λ=λ_c$ at the critical point. Such scaling property is valid also for time-dependent quantities such as the Loschmidt echo, provided time is measured in units of the inverse frequency of the critical mode.
We propose a simple model of coupled heat and particle transport based on a zero-dimensional classical deterministic dynamics which is reminiscent of a railway switch whose action is only a function of the particle's energy. It is shown that already in the minimal three-terminal model, where the second terminal is considered as a probe with zero net particle and heat currents, one can find extremely asymmetric Onsager matrices as a consequence of time-reversal symmetry breaking of the model. This minimalistic transport model provides a better understanding of thermoelectric heat engines in the presence of time-reversal symmetry breaking.
We report our investigations on the finite-size effects of the Lorenz number in a molecular wire. Using Landauer-Büttiker formalism, we find that for sufficiently long wires there are two validity regimes of the Wiedemann-Franz (WF) law, the cotunneling and the sequential tunneling regimes, while in small systems only the first regime survives. We compare our results with the standard Kubo formalism and explain its failure to detect the WF law in small systems. Furthermore, our studies on exponentially localized disordered wires show that the Lorenz number value L_0 predicted by the WF law is obtained only in the cotunneling regime. Also, the Lorenz number L exhibits a typical distribution at different temperatures corresponding to different tunneling process. In particular, first-order tunneling results in a low value of L whereas second-order tunneling recovers the universal value L_0.
We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the space of operators, and, for pure states, to twice the entropy of entanglement. The quantum to classical correspondence between the Wigner separability entropy and the separability entropy of the classical phase space Liouville density is illustrated by means of numerical simulations of chaotic maps. In this way, the separability entropy emerges as an extremely broad complexity quantifier in both the classical and quantum realms.
We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a "figure of merit" and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have simultaneously Carnot efficiency and non-zero power.
We show that when non-unitary noise effects are taken into account the thermopower is in general asymmetric under magnetic field reversal, even for non-interacting systems. Our findings are illustrated in the example of a three-dot ring structure pierced by an Aharonov-Bohm flux.
We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well known measure of complexity in classical systems and which is valid for both pure and mixed states in single-particle and many-body systems, takes into account the combined role of chaos and entanglement in the realm of quantum mechanics. The effectiveness of the measure is illustrated in the example of the Ising chain in a homogeneous tilted magnetic field. We provide numerical evidence that the multipartite entanglement generation leads to a linear increase of entropy until saturation in both integrable and chaotic regimes, so that in both cases the number of harmonics of the Wigner function grows exponentially with time. The entropy growth rate can be used to detect quantum phase transitions. The proposed entropy measure can also distinguish between integrable and chaotic many-body dynamics by means of the size of long term fluctuations which become smaller when quantum chaos sets in.
We study the coupled particle and energy transport in a prototype model of interacting one-dimensional system: the disordered hard-point gas, for which numerical data suggest that the thermoelectric figure of merit ZT diverges with the system size. This result is explained in terms of a microscopic mechanism, namely the local equilibrium is characterized by the emergence of a broad stationary "modified Maxwell-Boltzmann velocity distribution", of width much larger than the mean velocity of the particle flow.
The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this paper, we show that the diamond norm can be conveniently and in a physically transparent way computed by means of a Monte-Carlo algorithm based on the Fano representation of quantum states and quantum operations. The effectiveness of this algorithm is illustrated for several single-qubit quantum channels.
We study thermalization in many-body quantum systems locally coupled to an external bath. It is shown that quantum chaotic systems do thermalize, that is, they exhibit relaxation to an invariant ergodic state which, in the bulk, is well approximated by the grand canonical state. Moreover, the resulting ergodic state in the bulk does not depend on the details of the baths. On the other hand, for integrable systems the invariant state does depend on the bath and is different from the grand canonical state.
In this article we treat the subject of chaotic environments with few degrees of freedom in quantum communication by investigating a conservative dynamical map as a model of a dephasing quantum channel. When the channel's dynamics is chaotic, we investigate the model's semi-classical limit and show that the entropy exchange grows at a constant rate which depends on a single parameter (the interaction strength), analogous to stochastic models of dephasing channels. We analyze memory effects in the channel and present strong physical arguments to support that the present model is forgetful in the chaotic regime while memory effects in general cannot be ignored when channel dynamics is regular. In order to render the non-chaotic channel forgetful, it becomes necessary to apply a reset to the channel and this reset can efficiently be modeled by application of a chaotic map. We may then refer to encoding theorems (valid in the case of forgetful channels) to present evidence of a transition from noiseless to noisy channel due to the environment's transition from regular to chaotic dynamics.
We study the charge conductivity in one-dimensional prototype models of interacting particles, such as the Hubbard and the t-V spinless fermion model, when coupled to some external baths injecting and extracting particles at the boundaries. We show that, if these systems are driven far from equilibrium, a negative differential conductivity regime can arise. The above electronic models can be mapped into Heisenberg-like spin ladders coupled to two magnetic baths, so that charge transport mechanisms are explained in terms of quantum spin transport. The negative differential conductivity is due to oppositely polarized ferromagnetic domains which arise at the edges of the chain, and therefore inhibit spin transport: we propose a qualitative understanding of the phenomenon by analyzing the localization of one-magnon excitations created at the borders of a ferromagnetic region. We also show that negative differential conductivity is stable against breaking of integrability. Numerical simulations of non-equilibrium time evolution have been performed by employing a Monte-Carlo wave function approach and a matrix product operator formalism.
We show that the Fano representation leads to a particularly simple and appealing form of the quantum process tomography matrix $χ_{_F}$, in that the matrix $χ_{_F}$ is real, the number of matrix elements is exactly equal to the number of free parameters required for the complete characterization of a quantum operation, and these matrix elements are directly related to evolution of the expectation values of the system's polarization measurements. These facts are illustrated in the examples of one- and two-qubit quantum noise channels.
A Bose-Einstein condensate in an oscillating spatially asymmetric potential is shown to exhibit a directed current for unbiased initial conditions despite time symmetry. This phenomenon occurs only if the interaction between atoms, treated in mean-field approximation, exceeds a critical value. Our findings can be described with a three-mode model (TMM). These TMM results corroborate well with a many-body study over a time scale which increases with increasing atom number. The duration of this time scale probes the validity of the used mean-field approximation.
We show that, when a finite anisotropic Heisenberg spin-1/2 chain in the gapped regime is driven far from equilibrium, oppositely polarized ferromagnetic domains build up at the edges of the chain, thus suppressing quantum spin transport. As a consequence, a negative differential conductivity regime arises, where increasing the driving decreases the current. The above results are explained in terms of magnon localization and are shown to be structurally stable against breaking of integrability.
We propose a quantum algorithm for the purification of a generic mixed state $ρ$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii) the number of parameters which determine the purification state $|Ψ>$ exactly equals the number of degrees of freedom of $ρ$, and (iii) $|Ψ>$ is easily determined from the density matrix $ρ$. Moreover, we introduce a quantum circuit in which the quantum gates are unitary transformations acting on a $2n$-qudit system. These transformations are determined by parameters that can be tuned to generate, once the ancillary qudits are disregarded, any given mixed $n$-qudit state.
Any pure quantum state can be equivalently represented by means of its wave function psi(q) or of the Fermi function g_F(q,p), with q and p coordinates and conjugate momenta of the system under investigation.We show that a Gaussian wave packet can be conveniently visualized in phase space by means of the curve g_F(q,p)=0. The evolution in time of the g_F=0 curve is then computed for a Gaussian packet evolving freely or under a constant or a harmonic force. As a result, the spreading or shrinking of the packet is easily interpreted in phase space. Finally, we discuss a gedanken prism microscope experiment for measuring the position-momentum correlation. This gedanken experiment, together with the well-known Heisenberg microscope and von Neumann velocimeter, is sufficient to fully determine the state of a Gaussian packet.