scholarly journals Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Koji Hashimoto ◽  
Kyoung-Bum Huh ◽  
Keun-Young Kim ◽  
Ryota Watanabe
Keyword(s):  
Quantum Mechanics ◽  
High Temperature ◽  
Lyapunov Exponent ◽  
Harmonic Oscillator ◽  
Exponential Growth ◽  
Local Maximum ◽  
Detailed Examination ◽  
One Dimension ◽  
One Dimensional ◽  
Time Order

Abstract We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.

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 ADELIC HARMONIC OSCILLATOR

1995 ◽  
Vol 10 (16) ◽  
pp. 2349-2365 ◽  
Author(s):  
BRANKO DRAGOVICH
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Functional Relation ◽  
Vacuum State ◽  
One Dimensional ◽  
High Energies ◽  
The Riemann Zeta Function ◽  
Adelic Quantum Mechanics ◽  
Riemann Zeta ◽  
Very High

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered. It is a simple, exact and instructive adelic model. Eigenstates are Schwartz-Bruhat functions. The Mellin transform of the simplest vacuum state leads to the well-known functional relation for the Riemann zeta function. Some expectation values are calculated. The existence of adelic matter at very high energies is suggested.

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.

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.

Quantum mechanics on (anti)-de Sitter background

2017 ◽  
Vol 32 (26) ◽  
pp. 1750138 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
De Sitter ◽  
One Dimensional ◽  
Sitter Background ◽  
Extended Uncertainty

In this paper, the quantum mechanics on the (anti) de Sitter background is investigated. the extended uncertainty principle and the deformed calculus are discussed for the quantum mechanics on the (anti)-de Sitter background. As examples one-dimensional box problem and one-dimensional harmonic oscillator problem are discussed.

scholarly journals The one-dimensional harmonic oscillator damped with Caldirola-Kanai Hamiltonian

2018 ◽  
Vol 64 (1) ◽  
pp. 47
Author(s):  
Francis Segovia-Chaves
Keyword(s):  
Characteristic Function ◽  
Harmonic Oscillator ◽  
Canonical Transformation ◽  
Exponential Growth ◽  
Jacobi Equation ◽  
One Dimensional ◽  
Harmonic Motion ◽  
Damped Harmonic Oscillator ◽  
The One ◽  
Hamilton Jacobi Equation

In this paper, the solution to the Hamilton-Jacobi equation for the one-dimensional harmonic oscillator damped with the Caldirola-Kanai model is presented. Making use of a canonical transformation, we calculate the Hamilton characteristic function. It was found that the position of the oscillator shows an exponential decay similar to that of the oscillator with damping where the decay is more pronounced when increasing the damping constant γ. It is shown that when γ = 0, the behavior is of an oscillator with simple harmonic motion. However, unlike the damped harmonic oscillator where the linear momentum decays with time, in the case of the oscillator with the Caldirola-KanaiHamiltonian, the momentum increases as time increases due to an exponential growth of the mass m(t) = meγt.

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

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