Emergence of equilibrium thermodynamic properties in quantum pure states. II. Analysis of a spin model system

A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and of the equilibrium reduced density matrix of a subsystem for the two different statistics introduced in Part I. In order to analyze their consistency with thermodynamics, these quantities of interest are evaluated in the limit of large number of components of the isolated system. The main results can be summarized as follows: typical values of the entropy and of the equilibrium reduced density matrix as functions of the internal energy in the fixed expectation energy ensemble do not satisfy the requirement of thermodynamics. On the contrary, the thermodynamical description is recovered from the random pure state ensemble (RPSE), provided that one considers systems large enough. The thermodynamic limit of the considered properties for the spin system reveals a number of important features. First canonical statistics (and thus, canonical typicality as long as the fluctuations around the average value are small) emerges without the need of assuming the microcanonical space for the global pure state. Moreover, we rigorously prove (i) the equivalence of the "global temperature," derived from the entropy equation of state, with the "local temperature" determining the canonical state of the subsystems; and (ii) the equivalence between the RPSE typical entropy and the canonical entropy for the overall system.Comment: 30 pages, 10 figure

Pilot-wave quantum theory with a single Bohm's trajectory

The representation of a quantum system as the spatial configuration of its constituents evolving in time as a trajectory under the action of the wave-function, is the main objective of the Bohm theory. However, its standard formulation is referred to the statistical ensemble of its possible trajectories. The statistical ensemble is introduced in order to establish the exact correspondence (the Born's rule) between the probability density on the spatial configurations and the quantum distribution, that is the squared modulus of the wave-function. In this work we explore the possibility of using the pilot wave theory at the level of a single Bohm's trajectory. The pilot wave theory allows a formally self-consistent representation of quantum systems as a single Bohm's trajectory, but in this case there is no room for the Born's rule at least in its standard form. We will show that a correspondence exists between the statistical distribution of configurations along the single Bohm's trajectory and the quantum distribution for a subsystem interacting with the environment in a multicomponent system. To this aim, we present the numerical results of the single Bohm's trajectory description of the model system of six confined rotors with random interactions. We find a rather close correspondence between the coordinate distribution of one rotor along its trajectory and the time averaged marginal quantum distribution for the same rotor. This might be considered as the counterpart of the standard Born's rule. Furthermore a strongly fluctuating behavior with a fast loss of correlation is found for the evolution of each rotor coordinate. This suggests that a Markov process might well approximate the evolution of the Bohm's coordinate of a single rotor and it is shown that the correspondence between coordinate distribution and quantum distribution of the rotor is exactly verified

Signatures of Anderson localization and delocalized random quantum states

We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest model of a 1D disordered chain and we analyse both the dynamics of an initially localized state and the dynamics of quantum states drawn at random from the ensemble corresponding to the minimum knowledge about the initial state. While in the former case the site distribution remains confined in a limited portion of the chain, the site distribution of random pure state fluctuates around an equilibrium average that is delocalized over the entire chain. A clear connection between the equilibration observed when the system is initialized in a fully localized state and the amplitude of dynamical fluctuations of a typical random pure state is established

Beyond quantum microcanonical statistics

Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to consider the time evolution according to the unitary Schr\"odinger equation. On the other hand a mixed state, i.e. a statistical density matrix, is the standard formalism to account for thermal equilibrium, as postulated in the microcanonical quantum statistics. In the present paper an alternative treatment relying on a statistical analysis of the possible wavefunctions of an isolated system is presented. In analogy with the classical ergodic theory, the time evolution of the wavefunction determines the probability distribution in the phase space pertaining to an isolated system. However, this alone cannot account for a well defined thermodynamical description of the system in the macroscopic limit, unless a suitable probability distribution for the quantum constants of motion is introduced. We present a workable formalism assuring the emergence of typical values of thermodynamic functions, such as the internal energy and the entropy, in the large size limit of the system. This allows the identification of macroscopic properties independently of the specific realization of the quantum state. A description of material systems in agreement with equilibrium thermodynamics is then derived without constraints on the physical constituents and interactions of the system. Furthermore, the canonical statistics is recovered in all generality for the reduced density matrix of a subsystem

Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory

Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum systems. In the present contribution a simple but effective theoretical framework is introduced to clarify the connections between a purely mechanical description and the thermodynamic characterization of the equilibrium state of an isolated quantum system. A salient feature of our approach is the very transparent distinction between the statistical aspects and the dynamical aspects in the description of isolated quantum systems. Like in the classical statistical mechanics, the equilibrium distribution of any property is identified on the basis of the time evolution of the considered system. As a consequence equilibrium properties of quantum system appear to depend on the details of the initial state due to the abundance of constants of the motion in the Schr\"odinger dynamics. On the other hand the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. We shall consider two particular ensembles: the random pure state ensemble and the fixed expectation energy ensemble. The relation between the introduced ensembles, the properties of a given isolated system, and the standard quantum statistical description are discussed throughout the presentation. Finally we point out the conditions which should be satisfied by an ensemble in order to get meaningful thermodynamical characterization of an isolated quantum system.Comment: 30 pages, 1 figur

Typicality in Ensembles of Quantum States: Monte Carlo Sampling versus Analytical Approximations

Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics such as the emergence of well defined thermal properties from the pure quantum mechanical description of large many body systems. When dealing with an ensemble of pure quantum states, two questions naturally arise: what is the probability density function on the parameters which specify the state of the system in a given ensemble? And, does there exist a most typical value of a function of interest in the considered ensemble? Here two different ensembles are considered: the Random Pure State Ensemble (RPSE) and the Fixed Expectation Energy Ensemble (FEEE). By means of a suitable parameterization of the wave function in terms of populations and phases, we focus on the probability distribution of the populations in such ensembles. A comparison is made between the distribution induced by the inherent geometry of the Hilbert Space and an approximate distribution derived by means of the minimization of the informational functional. While the latter can be analytically handled, the exact geometrical distribution is sampled by a Metropolis-Hastings algorithm. The analysis is made for an ensemble of wavefunctions describing an ideal system composed of n spins 1/2 and reveals the salient differences between the geometrical and the approximate distributions. The analytical approximations are proven to be useful tools in order to obtain ensemble averaged quantity. In particular we focus on the distribution of the Shannon entropy by providing an explanation of the emergence of a typical value of this quantity in the ensembles.Comment: 27 pages, 7 figure

Identification of Design Principles for the Preparation of Colloidal Plexcitonic Materials

: Colloidal plexcitonic materials (CPMs) are a class of nanosystems where molecular dyes are strongly coupled with colloidal plasmonic nanoparticles, acting as nanocavities that enhance the light field. As a result of this strong coupling, new hybrid states are formed, called plexcitons, belonging to the broader family of polaritons. With respect to other families of polaritonic materials, CPMs are cheap and easy to prepare through wet chemistry methodologies. Still, clear structure-to-properties relationships are not available, and precise rules to drive the materials' design to obtain the desired optical properties are still missing. To fill this gap, in this article, we prepared a dataset with all CPMs reported in the literature, rationalizing their design by focusing on their three main relevant components (the plasmonic nanoparticles, the molecular dyes, and the capping layers) and identifying the most used and efficient combinations. With the help of statistical analysis, we also found valuable correlations between structure, coupling regime, and optical properties. The results of this analysis are expected to be relevant for the rational design of new CPMs with controllable and predictable photophysical properties to be exploited in a vast range of technological fields

Coherent electronic and nuclear dynamics in a rhodamine heterodimer-DNA supramolecular complex

Elucidating the role of quantum coherences in energy migration within biological and artificial multichromophoric antenna systems is the subject of an intense debate. It is also a practical matter because of the decisive implications for understanding the biological processes and engineering artificial materials for solar energy harvesting. A supramolecular rhodamine heterodimer on a DNA scaffold was suitably engineered to mimic the basic donor-acceptor unit of light-harvesting antennas. Ultrafast 2D electronic spectroscopic measurements allowed identifying clear features attributable to a coherent superposition of dimer electronic and vibrational states contributing to the coherent electronic charge beating between the donor and the acceptor. The frequency of electronic charge beating is found to be 970 cm-1 (34 fs) and can be observed for 150 fs. Through the support of high level ab initio TD-DFT computations of the entire dimer, we established that the vibrational modes preferentially optically accessed do not drive subsequent coupling between the electronic states on the 600 fs of the experiment. It was thereby possible to characterize the time scales of the early time femtosecond dynamics of the electronic coherence built by the optical excitation in a large rigid supramolecular system at a room temperature in solution. © 2017 the Owner Societies.Multi valued and parallel molecular logi

Hemodynamics in pig‐to‐baboon heterotopic thoracic cardiac xenotransplantation: Recovery from perioperative cardiac xenograft dysfunction and impairment by cardiac overgrowth

Introduction Orthotopic cardiac xenotransplantation has seen notable improvement, leading to the first compassionate use in 2022. However, it remains challenging to define the clinical application of cardiac xenotransplantation, including the back-up strategy in case of xenograft failure. In this regard, the heterotopic thoracic technique could be an alternative to the orthotopic procedure. We present hemodynamic data of heterotopic thoracic pig-to-baboon transplantation experiments, focusing on perioperative xenograft dysfunction and xenograft overgrowth. Methods We used 17 genetically modified piglets as donors for heterotopic thoracic xenogeneic cardiac transplantation into captive-bred baboons. In all animals, pressure probes were implanted in the graft's left ventricle and the recipient's ascending aorta and hemodynamic data (graft pressure, aortic pressure and recipient's heart rate) were recorded continuously. Results Aortic pressures and heart rates of the recipients’ hearts were postoperatively stable in all experiments. After reperfusion, three grafts presented with low left ventricular pressure indicating perioperative cardiac dysfunction (PCXD). These animals recovered from PCXD within 48 h under support of the recipient's heart and there was no difference in survival compared to the other 14 ones. After 48 h, graft pressure increased up to 200 mmHg in all 17 animals with two different time-patterns. This led to a progressive gradient between graft and aortic pressure. With increasing gradient, the grafts stopped contributing to cardiac output. Grafts showed a marked weight increase from implantation to explantation. Conclusion The heterotopic thoracic cardiac xenotransplantation technique is a possible method to overcome PCXD in early clinical trials and an experimental tool to get a better understanding of PCXD. The peculiar hemodynamic situation of increasing graft pressure but missing graft's output indicates outflow tract obstruction due to cardiac overgrowth. The heterotopic thoracic technique should be successful when using current strategies of immunosuppression, organ preservation and donor pigs with smaller body and organ size