A lower bound to exact energy levels for one-dimensional spin chains

1985 ◽  
Vol 20 (5) ◽  
pp. 562-564
Author(s):  
V. O. Cheranovskii
Keyword(s):  
Lower Bound ◽  
Energy Levels ◽  
Spin Chains ◽  
One Dimensional ◽  
Exact Energy

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

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 Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

Magnetic properties of manganese based one-dimensional spin chains

2015 ◽  
Vol 44 (46) ◽  
pp. 19812-19819 ◽  
Author(s):  
K. S. Asha ◽  
K. M. Ranjith ◽  
Arvind Yogi ◽  
R. Nath ◽  
Sukhendu Mandal
Keyword(s):  
Heat Capacity ◽  
Magnetic Properties ◽  
Magnetic Susceptibility ◽  
Spin Chains ◽  
One Dimensional

Magnetic susceptibility and heat capacity of three manganese based structures are measured and modeled with one-dimensional antiferromagnetic chains.

scholarly journals Energy levels of one-dimensional anharmonic oscillator via neural networks

2019 ◽  
Vol 34 (12) ◽  
pp. 1950088 ◽  
Author(s):  
Halil Mutuk
Keyword(s):  
Neural Network ◽  
Field Theory ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
High Accuracy ◽  
Network System ◽  
Quantum Field ◽  
One Dimensional ◽  
Neural Network System ◽  
Good Agreement

In this work, we obtained energy levels of one-dimensional quartic anharmonic oscillator by using neural network system. Quartic anharmonic oscillator is a very important tool in quantum mechanics and also in the quantum field theory. Our results are in good agreement in high accuracy with the reference studies.

scholarly journals SUBLINEARLY SPACE BOUNDED ITERATIVE ARRAYS

2010 ◽  
Vol 21 (05) ◽  
pp. 843-858 ◽  
Author(s):  
ANDREAS MALCHER ◽  
CARLO MEREGHETTI ◽  
BEATRICE PALANO
Keyword(s):  
Lower Bound ◽  
Computational Model ◽  
Regular Language ◽  
Finite Automata ◽  
Complexity Classes ◽  
Language Recognition ◽  
Deterministic Finite Automata ◽  
One Dimensional ◽  
Sequential Processing ◽  
Trade Offs

Iterative arrays (IAs) are a parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this paper, realtime-IAs with sublinear space bounds are used to recognize formal languages. The existence of an infinite proper hierarchy of space complexity classes between logarithmic and linear space bounds is proved. Some decidability questions on logarithmically space bounded realtime-IAs are investigated, and an optimal logarithmic space lower bound for non-regular language recognition on realtime-IAs is shown. Finally, some non-recursive trade-offs between space bounded realtime-IAs are emphasized.

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.

A NONLINEAR-OSCILLATOR MODEL FOR STRONG INTERACTION IN MOLECULAR SOLIDS

2006 ◽  
Vol 20 (30) ◽  
pp. 1953-1955 ◽  
Author(s):  
M. A. GRADO-CAFFARO ◽  
M. GRADO-CAFFARO
Keyword(s):  
Classical Limit ◽  
Vibrational Energy ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
Potential Interaction ◽  
Strong Interactions ◽  
Molecular Solids ◽  
One Dimensional ◽  
Vibrational Energy Levels ◽  
Type Potential

A theoretical model based upon a one-dimensional anharmonic oscillator is proposed in order to describe strong interactions in molecular solids. Vibrational energy levels are studied in terms of the associated vibrational quantum number; in particular, classical limit is discussed. Kinetic energy corresponding to a typical collision process is calculated. In addition, Morse-type potential interaction is found to be an approximation to our model.

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