79 research outputs found
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
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