Weight Construction in Extended Space Expectation Values for Singular Quantum Systems at Spectral Structuring and Temporal Constancy Limit

2014 ◽  
Author(s):  
Berfin Kalay ◽  
Metin Demiralp
Keyword(s):  
Quantum Systems ◽  
Expectation Values ◽  
Extended Space

scholarly journals Massively Parallel Classical Logic via Coherent Dynamics of an Ensemble of Quantum Systems with Dispersion in Size

2020 ◽  
Author(s):  
Hugo Gattuso ◽  
Raphael D. Levine ◽  
Francoise Remacle
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Algebraic Theory ◽  
Laser Pulses ◽  
Quantum Systems ◽  
Individual Variability ◽  
Expectation Values ◽  
Charge Transfer Excitons ◽  
Simultaneous Reading ◽  
Size Dispersion

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nano systems are not quite identical and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot, QD, dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semi-conducting QDs suggests that the dimer coherences can be probed at room temperature

scholarly journals Theory of temporal fluctuations in isolated quantum systems

2015 ◽  
Vol 29 (14) ◽  
pp. 1530008 ◽  
Author(s):  
Lorenzo Campos Venuti ◽  
Paolo Zanardi
Keyword(s):  
General Theory ◽  
Critical Region ◽  
Optical Lattice ◽  
Universal Function ◽  
Quantum Systems ◽  
Quantum Criticality ◽  
Expectation Values ◽  
Full Generality ◽  
Small Perturbations ◽  
Temporal Fluctuations

When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This paper reviews the general theory of such temporal fluctuations. We first survey some results on the strength of such temporal fluctuations. For example temporal fluctuations are exponentially small in the system's volume for generic systems whereas they fall-off algebraically in integrable systems. We then concentrate on the so-called quench scenario where the system is driven out-of-equilibrium under the application of a sudden perturbation. For sufficiently small perturbations, temporal fluctuations of physical observables can be characterized in full generality and can be used as an effective tool to probe quantum criticality of the underlying model. In the off-critical region the distribution becomes Gaussian. Close to criticality the distribution becomes a universal function uniquely characterized by a single critical exponent, that we compute explicitly. This contrasts standard equilibrium quantum fluctuations for which the critical distribution depends on a numerable set of critical coefficients and is known only for limited examples. The possibility of using temporal fluctuations to determine pseudo-critical boundaries in optical lattice experiments is further reviewed.

scholarly journals Massively Parallel Classical Logic via Coherent Dynamics of an Ensemble of Quantum Systems with Dispersion in Size

2020 ◽  
Author(s):  
Hugo Gattuso ◽  
Raphael D. Levine ◽  
Francoise Remacle
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Algebraic Theory ◽  
Laser Pulses ◽  
Quantum Systems ◽  
Individual Variability ◽  
Expectation Values ◽  
Charge Transfer Excitons ◽  
Simultaneous Reading ◽  
Size Dispersion

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nano systems are not quite identical and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot, QD, dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semi-conducting QDs suggests that the dimer coherences can be probed at room temperature

scholarly journals QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 617
Author(s):  
David Plankensteiner ◽  
Christoph Hotter ◽  
Helmut Ritsch
Keyword(s):  
Open Quantum Systems ◽  
Equations Of Motion ◽  
Mean Field ◽  
Quantum Systems ◽  
Cumulant Expansion ◽  
Field Equations ◽  
Expectation Values ◽  
Closed Set ◽  
Open Quantum ◽  
Mean Field Equations

A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled differential equations for operators in the Heisenberg picture. This typically leads to an infinite hierarchy of equations for products of operators. A well-established approach to truncate this infinite set at the level of expectation values is to neglect quantum correlations of high order. This is systematically realized with a so-called cumulant expansion, which decomposes expectation values of operator products into products of a given lower order, leading to a closed set of equations. Here we present an open-source framework that fully automizes this approach: first, the equations of motion of operators up to a desired order are derived symbolically using predefined canonical commutation relations. Next, the resulting equations for the expectation values are expanded employing the cumulant expansion approach, where moments up to a chosen order specified by the user are included. Finally, a numerical solution can be directly obtained from the symbolic equations. After reviewing the theory we present the framework and showcase its usefulness in a few example problems.

scholarly journals Degree of Quantumness in Quantum Synchronization

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
H. Eneriz ◽  
D. Z. Rossatto ◽  
F. A. Cárdenas-López ◽  
E. Solano ◽  
M. Sanz
Keyword(s):  
Quantum Information ◽  
Physical Properties ◽  
Quantum System ◽  
Figure Of Merit ◽  
Quantum Systems ◽  
Expectation Values ◽  
Van Der Pol ◽  
Superconducting Circuit ◽  
Quantum Synchronization ◽  
Van Der Pol Oscillators

AbstractWe introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators.

scholarly journals Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size

2020 ◽  
Vol 117 (35) ◽  
pp. 21022-21030 ◽  
Author(s):  
Hugo Gattuso ◽  
R. D. Levine ◽  
F. Remacle
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Algebraic Theory ◽  
Laser Pulses ◽  
Quantum Systems ◽  
Individual Variability ◽  
Expectation Values ◽  
Charge Transfer Excitons ◽  
Simultaneous Reading ◽  
Size Dispersion

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nanosystems are not quite identical, and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between theNlevels of a given quantum system can be handled as an observable. Thereby there areN2logic variables perNlevel system. This is how massive parallelism is achieved in that there areN2potential outputs for a quantum system ofNlevels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average theN2expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot (QD) dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimerNlevels include local and charge transfer excitons within each dimer. The well-studied physics of semiconducting QDs suggests that the dimer coherences can be probed at room temperature.

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