scholarly journals The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 44
Author(s):  
Kaushik Y. Bhagat ◽  
Baibhab Bose ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Rathindra N. Das ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Quantum Statistical Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Potential Well ◽  
One Dimensional ◽  
Quantum Randomness ◽  
The One ◽  
The Impact

The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both micro-canonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional Potential Well problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.

scholarly journals THE GENERALIZED OTOC FROM SUPERSYMMETRIC QUANTUM MECHANICS: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

2020 ◽  
Author(s):  
Sayantan Choudhury
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Quantum Statistical Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Potential Well ◽  
One Dimensional ◽  
Quantum Randomness ◽  
Random Fluctuations ◽  
The Impact

The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further we demonstrate an equivalent formalism of computation using a general time independent Hamiltonian having well defined eigenstate representation for integrable supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism we consider the two well known models viz. Harmonic Oscillator and one dimensional potential well within the framework of supersymmetry. For the Harmonic Oscillator case we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both microcanonical and canonical ensembles in quantum mechanics without supersymmetry. On the other hand, for one dimensional potential well problem we found significantly different time scale and the other parameter dependence compared to the results obtained from non-supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model independent Hamiltonian along with the previously mentioned these well cited models.

Quantum mechanics on (anti)-de Sitter background II: Ramsauer–Townsend effect and WKB method

2018 ◽  
Vol 33 (26) ◽  
pp. 1850150 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Harmonic Oscillator ◽  
Wkb Method ◽  
De Sitter ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Sitter Background ◽  
The One

Based on the one-dimensional quantum mechanics on (anti)-de Sitter background [W. S. Chung and H. Hassanabadi, Mod. Phys. Lett. A 32, 26 (2107)], we discuss the Ramsauer–Townsend effect. We also formulate the WKB method for the quantum mechanics on (anti)-de Sitter background to discuss the energy level of the quantum harmonic oscillator and quantum bouncer.

scholarly journals Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections

2019 ◽  
Vol 34 (04) ◽  
pp. 1950028
Author(s):  
R. D. Mota ◽  
D. Ojeda-Guillén ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Supersymmetric Quantum Mechanics ◽  
Type Model ◽  
One Dimensional ◽  
The Third ◽  
Derivative Formula ◽  
Supersymmetric Models ◽  
Oscillator Type ◽  
The Creation

By modifying and generalizing known supersymmetric models, we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of [Formula: see text]. Also, by changing the derivative [Formula: see text] by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator [Formula: see text], we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.

One-dimensional quantum mechanics with Dunkl derivative

2019 ◽  
Vol 34 (24) ◽  
pp. 1950190
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Scalar Product ◽  
Momentum Operator ◽  
Inner Product ◽  
One Dimensional ◽  
Coordinate Representation ◽  
The One ◽  
Infinite Wall

In this paper, we consider the quantum mechanics with Dunkl derivative. We use the Dunkl derivative to obtain the coordinate representation of the momentum operator and Hamiltonian. We introduce the scalar product to find that the momentum is Hermitian under this inner product. We study the one-dimensional box problem (the spin-less particle with mass m confined to the one-dimensional infinite wall). Finally, we discuss the harmonic oscillator problem.

Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Any Time Solution

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
M. A. Malkov
Keyword(s):  
Analytical Solution ◽  
Exact Analytical Solution ◽  
The Other ◽  
Longitudinal Impact ◽  
Infinite Plane ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Contact Surfaces ◽  
The One ◽  
The Impact

Using the Sobolev–Smirnov method, we have found the exact analytical solution of a longitudinal impact of semi-infinite plane elastic bars for any time after the impact. After collision, there are loading waves from contact surfaces of bars and unloading waves from lateral surfaces. Then the unloading waves reach the opposite surface of the bars and create the reflected loading waves. These loading waves reach the other surface of the bars and generate new unloading waves. The number of waves grows exponentially. The sum of waves tends to the wave of the one-dimensional approximation.

Orthogonalitätsrelationen der mehrzeitigen erzeugenden Funktionale des Harmonischen Oszillators

1971 ◽  
Vol 26 (2) ◽  
pp. 220-223 ◽  
Author(s):  
R Weber
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Scattering Theory ◽  
Functional Integration ◽  
One Dimensional ◽  
Eigen Values ◽  
The One

AbstractWe treat the one-dimensional harmonic oscillator completely in the field theoretic calculus of many time generating functionals. Without the results of common quantum mechanics we compute eigen values and functionals of the energy preparing all information of the harmonic oscillator. As an example of functional integration and for applications in scattering theory we prove orthonormality relations of these functionals.

On matrices whose eigenvalues are in arithmetic progression

1951 ◽  
Vol 47 (3) ◽  
pp. 585-590 ◽  
Author(s):  
P. T. Landsberg
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Arithmetic Progression ◽  
Matrix Elements ◽  
One Dimensional ◽  
The Matrix ◽  
The One ◽  
Matrix Problems ◽  
Image Position

The following matrix problems are well known in quantum mechanics:(a) The one-dimensional harmonic oscillator. Givendetermine the eigenvalues hjj of H, and the matrix elements of X, P if H is diagonal. It is found (Wigner (4)) that

Laughter on the Fringes

2019 ◽  
Author(s):  
Anna Peterson
Keyword(s):  
The Other ◽  
Literary Canon ◽  
Autobiographical Writing ◽  
Treasure Trove ◽  
Old Comedy ◽  
Other Hand ◽  
Aggressive Humor ◽  
The One ◽  
The Individual ◽  
The Impact

This book examines the impact that Athenian Old Comedy had on Greek writers of the Imperial era. It is generally acknowledged that Imperial-era Greeks responded to Athenian Old Comedy in one of two ways: either as a treasure trove of Atticisms, or as a genre defined by and repudiated for its aggressive humor. Worthy of further consideration, however, is how both approaches, and particularly the latter one that relegated Old Comedy to the fringes of the literary canon, led authors to engage with the ironic and self-reflexive humor of Aristophanes, Eupolis, and Cratinus. Authors ranging from serious moralizers (Plutarch and Aelius Aristides) to comic writers in their own right (Lucian, Alciphron), to other figures not often associated with Old Comedy (Libanius) adopted aspects of the genre to negotiate power struggles, facilitate literary and sophistic rivalries, and provide a model for autobiographical writing. To varying degrees, these writers wove recognizable features of the genre (e.g., the parabasis, its agonistic language, the stage biographies of the individual poets) into their writings. The image of Old Comedy that emerges from this time is that of a genre in transition. It was, on the one hand, with the exception of Aristophanes’s extant plays, on the verge of being almost completely lost; on the other hand, its reputation and several of its most characteristic elements were being renegotiated and reinvented.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

Sign in / Sign up

Export Citation Format

Share Document