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About 10,000 papers for “evolution operator”

FEL time-evolution operator

G. Dattoli, L. Giannessi, L. Mezi et al. · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · 1991

Cited by 23

Projection operator based expansion of the evolution operator

Vitalii Semin, Francesco Petruccione · Journal of Physics A Mathematical and Theoretical · 2016

The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative expression for the evolution operator, which differs from the traditional chronological exponent. An appropriate choice of projection operators results in the possibility of studying the diagonal and non-diagonal elements of the evolution operator separately. The suggested expression implies a particular form of perturbation expansion, which leads to a new formula for the short time dynamics. The new kind of perturbation expansion can be used to improve the accuracy of the usual chronological exponent significantly. The evolution operator for any arbitrary time can be efficiently recovered using the semigroup properties. The method is illustrated by two examples, namely the dynamics of a three-level system in two nonresonant laser fields and the calculation of the partition function of a finite XY-spin chain.

Cited by 0Open access

Using the Evolution Operator to Classify Evolution Algebras

D. Fernández-Ternero, Víctor M. Gómez-Sousa, Juan Núñez Valdés · Mathematical and Computational Applications · 2021

Evolution algebras are currently widely studied due to their importance not only “per se” but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of algebras and their applications. A criterion for classifying those satisfying certain conditions is given and an algorithm to obtain degenerate evolution algebras starting from those of smaller dimensions is also analyzed and constructed.

Cited by 3Open access

Evolution algebras whose evolution operator is a homomorphism

D. Fernández-Ternero, Víctor Manuel Gómez‐Sousa, Juan Núñez Valdés · Computational and Mathematical Methods · 2021

This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank n -2 and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made.

Cited by 1Open access

Quantum operator entropies under unitary evolution

Craig S. Lent · Physical review. E · 2019

For a quantum state undergoing unitary Schrödinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum operator entropy, which is the Shannon entropy of the probability distribution for the eigenvalues of a Hermitian operator [R. S. Ingarden, Quantum information theory, Rep. Math. Phys. 10, 43 (1976)RMHPBE0034-487710.1016/0034-4877(76)90005-7]. These entropies characterize the missing information about a particular observable inherent in the quantum state itself. The von Neumann entropy is the quantum operator entropy for the case when the operator is the density matrix. We examine pure state unitary evolution in a simple model system composed of a set of highly interconnected topologically disordered states and a time-independent Hamiltonian. An initially confined state is subject to free expansion into available states. The time development is completely reversible with no loss of quantum information and no course graining is applied. The positional entropy increases in time in a way that is consistent with both the classical statistical mechanical entropy and the second law.

Cited by 17Open access

The Operator Hierarchy: Evolution Beyond Genes

Gerard Jagers Op Akkerhuis · 2014

www.hypercycle.nl A proper understanding of the relationship between evolution, individuality and levels of biological organization, requires a fundamental approach to the recognition of what is an individual and what is a level of organization. Although many biologists have a tendency to focus exclusively on organisms and their genes as the eternal focal point of evolution, a universal perspective on evolution stretches much broader, including inanimate and animate particles alike and covering a continuous sequence of levels of organization, from physical particles, via organisms to future technical intelligences. In order to rephrase evolution on the basis of a particle hierarchy, the concept of a particle must be clearly defined. Many scientists think of particles as the entities that chemists and physicists investigate, decreasing in size from molecules and atoms to hadrons, quarks and gluons (Close, 1983; Pagels, 1985). Due to this abiotic bias, few regard bacteria as particles, let alone complex organisms such as plants and animals. To reconcile the worlds of physics and biology requires an overarching particle concept that is acceptable to both parties. This need was the reason for introducing a new

Cited by 0

Quantum operator entropies under unitary evolution

Lent, Craig S. · arXiv (Cornell University) · 2019

For a quantum state undergoing unitary Schrödinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum operator entropy, which is the Shannon entropy of the probability distribution for the eigenvalues of a Hermitian operator. These entropies characterize the missing information about a particular observable inherent in the quantum state itself. The von Neumann entropy is the quantum operator entropy for the case when the operator is the density matrix. We examine pure state unitary evolution in a simple model system comprised of a set of highly-interconnected topologically disordered states and a time-independent Hamiltonian. An initially confined state is subject to free expansion into available states. The time development is completely reversible with no loss of quantum information and no course graining is applied. The positional entropy increases in time in a way that is consistent with both the classical statistical mechanical entropy and the second law.

Cited by 0Open access

Spline-wavelet factorization for evolution operator

Carlo Cattani, Ettore Laserra, S. Tortoriello · Journal of Interdisciplinary Mathematics · 2004

Abstract In this paper, the wavelet solution of heat equation is considered and compared with spline approximation.

Cited by 0

Operator entanglement entropy of the time evolution operator in chaotic systems

Tianci Zhou, David J. Luitz · Physical review. B./Physical review. B · 2017

Entanglement entropy is a widely applicable indicator of the onset of quantum chaos. In particular, the entanglement entropy of the wave function after a quench from an initial state with low entanglement can be used to study the thermalization of the system. Here, the authors propose an initial-state independent quantity called the ``operator entanglement entropy'' (opEE) to extract the properties of the unitary evolution operator. They study the growth of the opEE in Floquet, chaotic, and many-body localized systems. They respectively have a linear, power-law, and logarithmic growth before reaching extensive saturation values. The most chaotic Floquet spin model has the maximal saturation value among the three classes and is identical to the value of a random unitary operator (the Page value). The authors interpret the opEE as the state EE of a quenched state living in a doubled Hilbert space, thus establishing its consistency with the existing state EE results. They conclude that the EE of the evolution operator should characterize the propagation of information in these systems.

Cited by 116Open access