Lecture 13: The N-Body Quantum System: Spectral Structure and Scattering

On the base of experimental data it was revealed that type of wave breaking depends on wave asymmetry against the vertical axis at wave breaking point. The asymmetry of waves is defined by spectral structure of waves: by the ratio between amplitudes of first and second nonlinear harmonics and by phase shift between them. The relative position of nonlinear harmonics is defined by a stage of nonlinear wave transformation and the direction of energy transfer between the first and second harmonics. The value of amplitude of the second nonlinear harmonic in comparing with first harmonic is significantly more in waves, breaking by spilling type, than in waves breaking by plunging type. The waves, breaking by plunging type, have the crest of second harmonic shifted forward to one of the first harmonic, so the waves have "saw-tooth" shape asymmetrical to vertical axis. In the waves, breaking by spilling type, the crests of harmonic coincides and these waves are symmetric against the vertical axis. It was found that limit height of breaking waves in empirical criteria depends on type of wave breaking, spectral peak period and a relation between wave energy of main and second nonlinear wave harmonics. It also depends on surf similarity parameter defining conditions of nonlinear wave transformations above inclined bottom.

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Maximization of the Uhlmann–Jozsa Fidelity for an Open Two-Level Quantum System with Coherent and Incoherent Controls

Physics of Particles and Nuclei ◽

10.1134/s1063779620040516 ◽

2020 ◽

Vol 51 (4) ◽

pp. 464-469

Author(s):

O. V. Morzhin ◽

A. N. Pechen’

Keyword(s):

Quantum System

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Thermodynamic Green’s Functions and Spectral Structure

10.1093/oso/9780198791942.003.0007 ◽

2018 ◽

Author(s):

Norman J. Morgenstern Horing

Keyword(s):

Green’S Function ◽

Green's Function ◽

Green's Functions ◽

Green’S Functions ◽

Spectral Weight ◽

Statistical Thermodynamic ◽

Spectral Structure ◽

Imaginary Time ◽

Translational Invariance ◽

The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

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Quantum Boxes, Stringed Instruments

10.1093/oso/9780198808275.003.0008 ◽

2017 ◽

Author(s):

Frank S. Levin

Keyword(s):

Energy Level ◽

Schrödinger Equation ◽

Quantum System ◽

Schrodinger Equation ◽

Probability Distributions ◽

Wave Functions ◽

Energy Level Diagram ◽

One Dimensional ◽

Stringed Instruments ◽

Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

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Quantum system compression: A Hamiltonian guided walk through Hilbert space

Physical Review A ◽

10.1103/physreva.103.012406 ◽

2021 ◽

Vol 103 (1) ◽

Cited By ~ 1

Author(s):

Robert L. Kosut ◽

Tak-San Ho ◽

Herschel Rabitz

Keyword(s):

Hilbert Space ◽

Quantum System

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How to Erase Quantum Monogamy?

Quantum Reports ◽

10.3390/quantum3010004 ◽

2021 ◽

Vol 3 (1) ◽

pp. 53-67

Author(s):

Ghenadie Mardari

Keyword(s):

Quantum System ◽

Quantum Entanglement ◽

The Other ◽

Arrow Of Time ◽

Quantum Level ◽

Delayed Choice ◽

Other Hand ◽

The One ◽

Quantum Erasure ◽

Non Locality

The phenomenon of quantum erasure exposed a remarkable ambiguity in the interpretation of quantum entanglement. On the one hand, the data is compatible with the possibility of arrow-of-time violations. On the other hand, it is also possible that temporal non-locality is an artifact of post-selection. Twenty years later, this problem can be solved with a quantum monogamy experiment, in which four entangled quanta are measured in a delayed-choice arrangement. If Bell violations can be recovered from a “monogamous” quantum system, then the arrow of time is obeyed at the quantum level.

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