1,721,024 research outputs found
Typicality, Fluctuations and Quantum Dynamics: Statistical Mechanics of Quantum Systems
Full text linkRecently, the possibility of investigating single molecule, or single spin observables, as well as the necessity of a better understanding of the mechanisms underlying quantum dynamics in order to obtain nanoscale devices and nanostructered materials suitable for quantum computing tasks, have revived the interest in foundational aspects of quantum statistical mechanics. This thesis aims to give a contribution to this field by re-considering the statistical characterization of a quantum system at the light of some paradigmatic changes in our understanding of quantum theory which have taken place in the last two decades. In particular the impressive development of quantum information theory has changed the perceptions of quantum entanglement: for a long time it has been considered a somewhat paradoxical property of the matter at the atomic scale, but now it is regarded as an essential and ubiquitous phenomenon whose consequences are affecting the very macroscopic world that we experience. Still the decoherence program has brought out the importance of considering a quantum system together with its environment in order to clarify some key aspects of quantum dynamics. Thus, we start from the idea that quantum correlations are ubiquitous and somewhat uncontrollable in systems with many degrees of freedom which are typically considered in statistical mechanics. As a consequence we assume the standpoint that quantum statistical mechanics has not to be based on the underlying idea of a collection of many, independent quantum systems but rather it has to emerge at the level of a global wavefunction (pure state) which describes the system as well as its environment as a whole.
In order to investigate the consequences of these assumptions we study the equilibrium distribution of an isolated quantum system. This is defined, in analogy with the ergodic foundations of classical statistical mechanics, on the basis of the time evolution of the quantum state. Then, we study the emergence of thermodynamic properties in a quantum system by studying the probability distribution of some function of interests, as the entropy and the equilibrium state of a subsystem, on Ensembles of Pure States. Such a probability distribution is derived from the geometry of the Hilbert space, and the theoretical tools suitable for its characterization are developed. On the one hand we perform a numerical sampling of the ensemble distributions by employing Monte Carlo techniques, on the other hand simpler analytical approximation of the geometrical distributions are derived by means of a maximum entropy principle.
Model systems composed of an ensemble of spins are chosen to illustrate the salient features which emerge from the developed theoretical framework: the main point is that the Ensemble Distributions of “thermodynamic observables” (entropy or equilibrium state of a subsystem) are sharply peaked around a typical value. From the analysis it emerges that each of the overwhelming majority of the wavefunctions which has appreciable weight in the considered ensemble, is characterized by the same value of the “macroscopic” functions. This is a striking evidence of the “typicality” of these properties. In the essence, our impossibility to know the state of the system in detail does not matter, just for the remarkable fact that almost all quantum states behave essentially in the same way. By virtue of this typicality the study of the behaviour of the typical values of the thermodynamic function become meaningful. Notably, under certain conditions, one recovers the results of standard statistical mechanics, that is, the equilibrium average of the state of a subsystem can be cast in the Boltzmann canonical form at the temperature given by the usual thermodynamical relation .
In the second part of the thesis we consider the dynamical aspects of the equilibrium state of a subsystem interacting with its environment. The fluctuations around the equilibrium average critically depends on the entanglement between the system and the environment and on the form of the interaction Hamiltonian. The connection between the dynamics of the fluctuations of an observable at the equilibrium and the relaxation toward the equilibrium from a “non typical” initial value is also investigated with the aid of simple model systems.
The study presented in this thesis was partly motivated by a critical analysis of the statistical methods available for the theoretical modelling of magnetic resonance experiments. One of these, the Stochastic Liouville Equation, has been employed in a work completed during the first year of my Ph.D. program in order to interpret some feature of a two dimensional electron spin resonance experiment, [Fresch B., Frezzato D., Moro G. J., Kothe G., Freed J. H.; J. Phys. Chem. B., 110, 24238, (2006)].Nuove tecnologie hanno reso possibile lo studio spettroscopico di proprietà di singola molecola e di singolo spin, inoltre, gli avanzamenti nel campo delle nanotecnologie, mettono costantemente alla prova la nostra comprensione dei meccanismi che governano la dinamica a livello quantistico. Questi recenti sviluppi stanno rinnovando l’interesse intorno a questioni fondamentali non pienamente comprese e risolte; una di queste questioni riguarda i fondamenti della meccanica statistica quantistica. Lo scopo della presente tesi è quello di dare un contributo in questo affascinante campo, alla luce degli importanti cambiamenti avvenuti negli ultimi vent’ anni nella nostra comprensione della meccanica quantistica. In particolare gli studi condotti nell’ambito della teoria dell’informazione hanno profondamente modificato la nostra percezione dell’ entanglement quantistico. Questo è stato per lungo tempo considerato una proprietà quasi paradossale della materia su scala atomica mentre oggi è ritenuto un fenomeno essenziale e onnipresente importante per comprendere l’emergere del mondo macroscopico così come lo conosciamo. Inoltre, la formulazione e lo sviluppo del cosiddetto “decoherence program” ha introdotto un nuovo paradigma nella descrizione dell’evoluzione temporale dei sistemi quantistici riconoscendo il ruolo fondamentale dell’interazione con l’ambiente nel determinare aspetti essenziali della dinamica. Assumendo una prospettiva in linea con questi progressi, in questa tesi si parte dall’idea che la correlazione quantistica, l’entanglement, non possa essere ignorata nel derivare una descrizione statistica coerente dei sistemi complessi tradizionalmente considerati in meccanica statistica. La logica conseguenza di questo punto di vista è che la meccanica statistica quantistica non possa essere basata sull’idea dell’esistenza di insiemi di sistemi quantistici fra loro indipendenti, ma al contrario debba emergere dalla descrizione in termini di una singola funzione d’onda (stato puro) che descrive il sistema nella sua globalità, i.e. il sottosistema di interesse insieme con il suo ambiente (“environment”).
Allo scopo di costruire tale descrizione, in questa tesi si considera in primo luogo la distribuzione di probabilità che descrive lo stato di equilibrio di un sistema quantistico isolato. Essa è definita, in analogia con la teoria ergodica classica, sulla base dell’evoluzione temporale del sistema. Per studiare l’emergere delle proprietà termodinamiche si introducono poi distribuzioni di probabilità su insiemi di stati puri (“Ensemble Distributions”). Tali distribuzioni sono derivate sulla base della geometria dello spazio di Hilbert che descrive il sistema nella sua interezza. Inoltre si sono sviluppati gli strumenti teorici che permettono la caratterizzazione di tali distribuzioni di probabilità: essi consistono da un lato nell’implementazione di metodi numerici di tipo Monte Carlo che permettono il campionamento statistico diretto delle distribuzioni, d’altro canto sono state sviluppate approssimazioni analitiche delle distribuzioni sulla base del principio di massima entropia.
I risultati fondamentali che emergono dal quadro teorico sviluppato sono illustrati mediante lo studio della statistica in sistemi di spin: il messaggio fondamentale è che le funzioni termodinamiche, come l’entropia del sistema globale e lo stato di equilibrio di un sottosistema, sono caratterizzate da distribuzioni sull’ ensemble che risultano molto concentrate intorno ad un valore tipico. Dall’analisi condotta si deduce quindi che ognuno dei singoli stati puri considerati nell’insieme è caratterizzato dallo stesso valore delle funzioni termodinamiche studiate. Questa è una chiara evidenza della proprietà di tipicalità, (“typicality”), di queste funzioni. L’essenza di questo risultato è che la nostra incapacità di conoscere i dettagli dello stato quantistico del sistema non è così importante dal momento che la grande maggioranza dei possibili stati che appartengono all’insieme considerato sono caratterizzati dallo stesso valore delle proprietà termodinamiche alle quali siamo interessati. In virtù di tale proprietà risulta sensato studiare gli andamenti dei valori tipici delle proprietà termodinamiche. Sotto certe condizioni si ritrovano i risultati della meccanica statistica standard: in particolare lo stato di equilibrio di un sottosistema risulta essere in media lo stato canonico di Boltzmann alla temperatura definita dall’usuale relazione termodinamica .
Nella seconda parte della tesi, invece, si illustra la dinamica associata allo stato di equilibrio di un sistema in interazione con il suo ambiente. Le caratteristiche delle fluttuazioni intorno ai valori medi di equilibrio dipendono sia dall’entanglement tra il sistema e l’ambiente che dal tipo di interazione considerato. Per finire si considera la connessione fra la dinamica delle fluttuazioni all’equilibrio e i processi di rilassamento da uno stato iniziale di non equilibrio.
Il lavoro presentato in questa tesi è stato in parte motivato da un analisi critica dei metodi stocastici utilizzati nella modellizzazione teorica delle spettroscopie magnetiche. Durante il primo anno di dottorato tali metodologie sono state impiegate per l’interpretazione di alcune osservabili in esperimenti di risonanza magnetica elettronica bidimensionale. [Fresch B., Frezzato D., Moro G. J., Kothe G., Freed J. H.; J. Phys. Chem. B., 110, 24238, (2006)]
LA BANDA DEI CHIMICI
No full textSi può accendere una lampadina con un limone?
E creare un piccolo vulcano usando l'aceto?
Tra molecole parlanti e atomi che camminano, Emilio e la sua banda vivono curiose avventure nel mondo della chimica, scoprono i misteri di alcuni fenomeni scientifici e si divertono a sperimentare all'ombra degli alberi di un parco. Ma un imprevisto rovina la crescita di alcuni cristalli e la banda di amici deve vedersela con un paio di intrusi..
Typicality of the response by quantum pure states
No full textTypicality of the response by quantum pure states
Barbara Fresch, Giorgio J. Moro
Dipartimento di Science Chimiche, Università di Padova, via Marzolo 1, 35131
Padova, Italy
Mainly because of the objective of realizing quantum computers, in recent years an
intense research activity has been developed about the statistical and dynamical
properties of quantum pure states, that is of quantum systems without entanglement
with the environment. In such a framework several fundamental issues have been
risen, concerning for instance the description of equilibrium properties [1-4].
Indeed, in opposition to standard microcanonical quantum description, one has to
take into account that different quantum pure states, with well defined sets of
populations for the Hamiltonian eigenstates [5], are compatible with a given
macrostate. We have proposed the Random Pure State Ensemble (RPSE) as the
self-consistent statistical ensemble of quantum pure states, which is able to
generate a macroscopic description in agreement with thermodynamics [6,7]. More
recently we have analyzed the predictions of RPSE statistics in presence of an
external time dependent field, in order to test its capability of supplying the correct
framework for the study of dynamical properties [8]. Several important features
emerge from the simulations of spin systems, like the relaxation after a quench. It is
shown that typicality of equilibrium states is generalized to the response, so that the
dynamical properties become independent of the particular realization of the
quantum pure state.
[1] J. Gemmer, M. Michel, G. Mahler, Quantum Thermodynamics (Springer,
New York, 2004).
[2] S. Goldestein, J.L. Lebowitz, R. Tumulka, N. Zanghi, Phys. Rev. Lett. 96
(2006), 050403; S. Goldstein, J.L. Lebowitz, C. Mastrodonato, R. Tumulka,
N. Zanghi, Phys. Rev. E 81 (2010), 0111098.
[3] S. Popescu, A.J. Short, A. Winter, Nature Phys. 2 (2006); N. Linden, S.
Popescu, A.J. Short, A. Winter, Phys. Rev. E 79 (2009), 055021.
[4] P. Reiman, Phys. Rev. Lett. 99 (2007) 160404, Phys. Rev. Lett. 101 (2008)
190403.
[5] B. Fresch and G. J. Moro, J. Phys. Chem. A 113 (2009), 14502.
[6] B. Fresch and G. J. Moro J. Chem. Phys. 133 (2010), 034509, 034510.
[7] B. Fresch and G. J. Moro, J. Chem. Phys. 134 (2011), 054510.
[8] B. Fresch and G. J. Moro, (2011) arXiv:1104.4625
Atomistic account of structural and dynamical changes induced by small binders in the double helix of a short DNA
No full textpeer reviewe
Tuning the Properties of Pd Nanoclusters by Ligand Coatings: Electronic Structure Computations on Phosphine, Thiol, and Mixed PhosphineThiol Ligand Shells
No full textpeer reviewedTuning the properties of Palladium nanoparticles using different protecting ligand shells is an important step toward the application-orientated design of nanoparticles for nano-electronics and catalysis. We present a density functional theoretical characterization of Pd13 and Pd55 metal cores protected by only-thiol, only-phosphine and mixed phosphine-thiol ligand shells. We analyze the ligand contributions to the frontier orbitals and the charge redistribution between the ligand shell and the metal core and show that these properties control the values of the charging energy and the catalytic activity. The charge transfer character of the metal-ligand interaction is influenced by the presence of other ligands in the capping system indicating a cooperative effect in the ligand induced charge redistribution. Because of the interplay between the stabilization of the frontier orbital due to the contribution of the sulfur and the charge donation by the phosphine, the charging energy of the mixed phosphine-thiol protected cluster is larger than that of the only-phosphine and the only-thiol systems. The complementary point of view is adopted for rationalizing the catalytic properties of the clusters by analyzing the effect of the interaction with the metallic core on the properties of the ligand. The impact of solvation on the electronic structure of the ligand capped Pd13 cluster is investigated by including explicitly a layer of water molecules in the model system
Typicality in Ensembles of Quantum States: Monte Carlo Sampling versus Analytical Approximations
No full textpeer reviewe
Spectral shift, electronic coupling and exciton delocalization in nanocrystal dimers: insights from all-atom electronic structure computations
Full text linkDelocalization of excitons promoted by electronic coupling between clusters or quantum dots (QD) changes the dynamical processes in nanostructured aggregates enhancing energy transport. A spectroscopic shift of the absorption spectrum upon QD aggregation is commonly observed and ascribed to quantum mechanical coupling between neighbouring dots but also to exciton delocalization over the sulphur-based ligand shell or to other mechanisms as a change in the dielectric constant of the surrounding medium. We address the question of electronic coupling and exciton delocalization in nanocrystal aggregates by performing all-atom electronic structure calculations in models of colloidal QD dimers. The relation between spectral shift, interdot coupling and exciton delocalization is investigated in atomistic detail in models of dimers formed by CdSe clusters kept together by bridging organic ligands. Our results support the possibility of obtaining exciton delocalization over the dimer and point out the crucial role of the bridging ligand in enhancing interdot electronic coupling
A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy
No full textMultidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models
Pilot-Wave Quantum Theory with a Single Bohm’s Trajectory
Full text linkThe 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 de Broglie–Bohm theory (or pilot wave 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, that is a single realization of the time dependent configuration which should be representative of a single realization of the quantum system. 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 planar rotors with random interactions. We find a rather close correspondence between the coordinate distribution of one rotor, the others representing the environment, 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 when the pilot wave theory is applied at the level of single Bohm’s trajectory. 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 (the subsystem) and, under this condition, it is shown that the correspondence between coordinate distribution and quantum distribution of the rotor is exactly verified
Simulating action-2D electronic spectroscopy of quantum dots: insights on the exciton and biexciton interplay from detection-mode and time-gating
Full text link- …
