Efficient Numerical Solution of Time-Dependent Multichannel One-Dimensional or Radial Problems In Quantum Mechanics

2009 ◽  
Author(s):  
Karel Houfek ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Quantum Mechanics ◽  
Numerical Solution ◽  
Time Dependent ◽  
One Dimensional

scholarly journals TIME-DEPENDENT PARASUPERSYMMETRY IN QUANTUM MECHANICS

1996 ◽  
Vol 11 (26) ◽  
pp. 2095-2104 ◽  
Author(s):  
BORIS F. SAMSONOV
Keyword(s):  
Quantum Mechanics ◽  
Discrete Spectrum ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Time Dependent ◽  
Darboux Transformations ◽  
Integral Of Motion ◽  
One Dimensional ◽  
A Chain ◽  
The One

Parasupersymmetry of the one-dimensional time-dependent Schrödinger equation is established. It is intimately connected with a chain of the time-dependent Darboux transformations. As an example a parasupersymmetric model of nonrelativistic free particle with threefold degenerate discrete spectrum of an integral of motion is constructed.

scholarly journals ATTAINABLE ELECTRON ENERGY IN DIODE WITH PLASMA CATHODE AT THE GIVEN VOLTAGE

2019 ◽  
pp. 100-105
Author(s):  
V. Ostroushko ◽  
A. Pashchenko ◽  
I. Pashchenko
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Electron Energy ◽  
Time Dependent ◽  
Forward Motion ◽  
Plasma Cathode ◽  
One Dimensional ◽  
The Given

It is considered an acceleration of electrons in a one-dimensional interval, part of which is filled by ions initially compensated by electrons. For the stages of forward motion and backward motion of a part of electrons, the problem is reduced to a numerical solution of ordinary differential equations for some set of time-dependent quantities. The ratio of attainable energy to the energy corresponding to the voltage is maximum and near to 1.87475 for relatively small values of the width of the space without ions when applying a certain voltage, which, as the width is reduced, has to be reduced as a width cube.

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.

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