Ground and excited states of one-dimensional self-interacting nonlinear oscillators through time-dependent quantum mechanics

2003 ◽  
Vol 91 (5) ◽  
pp. 597-606 ◽  
Author(s):  
Amita Wadehra ◽  
Amlan K. Roy ◽  
B. M. Deb
Keyword(s):  
Quantum Mechanics ◽  
Excited States ◽  
Nonlinear Oscillators ◽  
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.

Quantum Mechanics / Extremely Localized Molecular Orbital Embedding Strategy for Excited-States. 1. Coupling to Time-Dependent Density Functional Theory

2020 ◽  
Author(s):  
Giovanni Macetti ◽  
Alessandro Genoni
Keyword(s):  
Density Functional Theory ◽  
Quantum Mechanics ◽  
Excited States ◽  
Quantum Chemical ◽  
Density Functional ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Functional Theory ◽  
Large Systems ◽  
Dependent Density

The QM/ELMO (quantum mechanics / extremely localized molecular orbital) method is a recently developed embedding technique in which the most important region of the system under exam is treated at fully quantum mechanical level, while the rest is described by means of transferred and frozen extremely localized molecular orbitals. In this paper, we propose the first application of the QM/ELMO approach to the investigation of excited-states and, in particular, we present the coupling of the QM/ELMO philosophy with Time-Dependent Density Functional Theory (TDDFT). The proposed TDDFT/ELMO strategy has been subjected to a series of preliminary tests that were already considered for the validations of other embedding TDDFT methods. The obtained results show that the novel technique allows the accurate description of local excitations in large systems by only including a relatively small group of atoms in the region treated at fully quantum chemical level. Furthermore, it was observed that, even using functionals that do not take into account long-range corrections, the method enables to avoid the presence of artificial low-lying charge-transfer states that may affect traditional TDDFT calculations. Finally, through the application to a reduced model of the Green Fluorescent Protein, it was proved that the TDDFT/ELMO approach can be also successfully exploited to investigate local electronic transitions in large systems and that the accuracy of the results can be improved by including a sufficient number of fragments/residues that are chemically crucial in the quantum mechanical region. This work paves the way to further extensions of the QM/ELMO philosophy for the study of local excitations in extended systems, suggesting the coupling of the QM/ELMO approach with other quantum chemical methods for excited-states, from the simplest ΔSCF techniques to the most advanced and computationally expensive multi-references methods.

Quantum Mechanics / Extremely Localized Molecular Orbital Embedding Strategy for Excited-States. 1. Coupling to Time-Dependent Density Functional Theory

2020 ◽  
Author(s):  
Giovanni Macetti ◽  
Alessandro Genoni
Keyword(s):  
Density Functional Theory ◽  
Quantum Mechanics ◽  
Excited States ◽  
Quantum Chemical ◽  
Density Functional ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Functional Theory ◽  
Large Systems ◽  
Dependent Density

The QM/ELMO (quantum mechanics / extremely localized molecular orbital) method is a recently developed embedding technique in which the most important region of the system under exam is treated at fully quantum mechanical level, while the rest is described by means of transferred and frozen extremely localized molecular orbitals. In this paper, we propose the first application of the QM/ELMO approach to the investigation of excited-states and, in particular, we present the coupling of the QM/ELMO philosophy with Time-Dependent Density Functional Theory (TDDFT). The proposed TDDFT/ELMO strategy has been subjected to a series of preliminary tests that were already considered for the validations of other embedding TDDFT methods. The obtained results show that the novel technique allows the accurate description of local excitations in large systems by only including a relatively small group of atoms in the region treated at fully quantum chemical level. Furthermore, it was observed that, even using functionals that do not take into account long-range corrections, the method enables to avoid the presence of artificial low-lying charge-transfer states that may affect traditional TDDFT calculations. Finally, through the application to a reduced model of the Green Fluorescent Protein, it was proved that the TDDFT/ELMO approach can be also successfully exploited to investigate local electronic transitions in large systems and that the accuracy of the results can be improved by including a sufficient number of fragments/residues that are chemically crucial in the quantum mechanical region. This work paves the way to further extensions of the QM/ELMO philosophy for the study of local excitations in extended systems, suggesting the coupling of the QM/ELMO approach with other quantum chemical methods for excited-states, from the simplest ΔSCF techniques to the most advanced and computationally expensive multi-references methods.

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 Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

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