scholarly journals A resurgence analysis for cubic and quartic anharmonic potentials

2017 ◽  
Vol 32 (05) ◽  
pp. 1750033 ◽  
Author(s):  
Ilmar Gahramanov ◽  
Kemal Tezgin
Keyword(s):  
Quantum Mechanics ◽  
Energy Levels ◽  
Resonance Energy ◽  
One Dimensional

In this work, we explicitly show resurgence relations between perturbative and one instanton sectors of the resonance energy levels for cubic and quartic anharmonic potentials in one-dimensional quantum mechanics. Both systems satisfy the Dunne–Ünsal relation and hence we are able to derive one-instanton nonperturbative contributions with the fluctuation terms to the energy merely from the perturbative data. We confirm our results with previous results obtained in the literature.

scholarly journals Tutorial: The quantum finite square well and the Lambert W function

2017 ◽  
Vol 95 (2) ◽  
pp. 105-110 ◽  
Author(s):  
Ken Roberts ◽  
S.R. Valluri
Keyword(s):  
Quantum Mechanics ◽  
Energy Levels ◽  
Inverse Image ◽  
Lambert W Function ◽  
Infrared Photodetector ◽  
Additional Insight ◽  
One Dimensional ◽  
Quantum Well Infrared Photodetector ◽  
Square Well ◽  
Insight Into

We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping w → z = wew between two complex domains. The solution of the finite square well problem can be seen to be described by the images of simple geometric shapes, lines, and circles, under this map and its inverse image. The technique can also be described using the Lambert W function. One can work in either of the complex domains, thereby obtaining additional insight into the finite square well problem and its bound energy states. This suggests interesting possibilities for the design of materials that are sensitive to minute changes in their environment such as nanostructures and the quantum well infrared photodetector.

scholarly journals AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Riemann Surface ◽  
Central Charge ◽  
Global Solutions ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

scholarly journals Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Quantum Interference ◽  
Direct Detection ◽  
Energy Levels ◽  
Vacuum Fluctuations ◽  
Heavy Particles ◽  
Evolving Systems ◽  
Gedanken Experiment ◽  
Classical Computer

AbstractFast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be the vacuum fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an inexplicable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment.

THE ANALOGUE OF THE AHARONOV–BOHM EFFECT FOR BOUND STATES FOR NEUTRAL PARTICLES

2011 ◽  
Vol 26 (18) ◽  
pp. 1331-1341 ◽  
Author(s):  
KNUT BAKKE ◽  
C. FURTADO
Keyword(s):  
Bound States ◽  
Neutral Particle ◽  
Energy Levels ◽  
Quantum Ring ◽  
Persistent Currents ◽  
One Dimensional ◽  
Neutral Particles ◽  
Quantum Flux ◽  
Bohm Effect ◽  
Aharonov Bohm

We study the analogue of the Aharonov–Bohm effect for bound states for a neutral particle with a permanent magnetic dipole moment interacting with an external field. We consider a neutral particle confined to moving between two coaxial cylinders and show the dependence of the energy levels on the Aharonov-Casher quantum flux. Moreover, we show that the same flux dependence of the bound states can be found when the neutral particle is confined to a one-dimensional quantum ring and a quantum dot, and we also calculate the persistent currents in each case.

scholarly journals Splitting of degenerate states in one-dimensional quantum mechanics

2012 ◽  
Vol 127 (3) ◽  
Author(s):  
Avik Dutt ◽  
Trisha Nath ◽  
Sayan Kar ◽  
Rajesh Parwani
Keyword(s):  
Quantum Mechanics ◽  
One Dimensional ◽  
Degenerate States

scholarly journals p-Adic Path Integrals for Quadratic Actions

1997 ◽  
Vol 12 (20) ◽  
pp. 1455-1463 ◽  
Author(s):  
G. S. Djordjević ◽  
B. Dragovich
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Path Integrals ◽  
Probability Amplitude ◽  
Exact Form ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
One Dimensional ◽  
Ordinary Quantum

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude [Formula: see text] for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.

R-matrix calculations of photoionization cross section of Ne-like tungsten

2015 ◽  
Vol 93 (11) ◽  
pp. 1221-1226 ◽  
Author(s):  
Indu Khatri ◽  
Arun Goyal ◽  
Sunny Aggarwal ◽  
A.K. Singh ◽  
Man Mohan
Keyword(s):  
Cross Section ◽  
Energy Levels ◽  
Resonance Energy ◽  
Photoionization Cross Section ◽  
Distorted Wave ◽  
Rydberg Series ◽  
Close Coupling ◽  
R Matrix ◽  
Coupling Approximation ◽  
Wave Methods

The photoionization cross section calculation for the ground state 1s22s22p6 1S (J = 0) of Ne-like W64+ has been performed in the close-coupling approximation using the Dirac–Coulomb R-matrix method. The resonance structures are analysed and described by finding the resonance energy positions of prominent Rydberg series 2s2p6(2S)np 1P0 for W LXV ion. To calculate fine structure energy levels, multi-configuration Dirac–Fock and relativistic distorted-wave methods have been employed. Wherever possible we have compared our work with the available data. The present results will be useful for diagnostics and modeling of plasma in ITER and other fusion devices.

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