scholarly journals Analytical and numerical analysis of the complete Lipkin–Meshkov–Glick Hamiltonian

2018 ◽  
Vol 27 (05) ◽  
pp. 1850039 ◽  
Author(s):  
Giampaolo Co’ ◽  
Stefano De Leo
Keyword(s):  
Lower Energy ◽  
Energy Gap ◽  
Energy Levels ◽  
Body System ◽  
Many Body ◽  
Energy Eigenvalues ◽  
Lower Energy Level ◽  
First Excited State ◽  
Text Interaction ◽  
The Many

The Lipkin–Meshkov–Glick is a simple, but not trivial, model of a quantum many-body system which allows us to solve the many-body Schrödinger equation without making any approximation. The model, which in its unperturbed case is composed only by two energy levels, includes two interacting terms. A first one, the [Formula: see text] interaction, which promotes or degrades pairs of particles, and a second one, the [Formula: see text] interaction, which scatters one particle in the upper and another in the lower energy level. In comparing this model with other approximation methods, the [Formula: see text] term interaction is often set to zero. In this paper, we show how the presence of this interaction changes the global structure of the system, generates degeneracies between the various eigenstates and modifies the energy eigenvalues structure. We present analytical solutions for systems of two and three particles and, for some specific cases, also for four, six and eight particles. The solutions for systems with more than eight particles are only numerical but their behavior can be well understood by considering the extrapolations of the analytical results. Of particular interest is the study of how the [Formula: see text] interaction affects the energy gap between the ground state and the first-excited state.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

ENERGY DIGESTIBILITY AND NITROGEN RETENTION BY PIGS AND RATS FED DIETS CONTAINING NON-NUTRITIVE DILUENTS AND VARYING IN PROTEIN LEVEL

1961 ◽  
Vol 41 (1) ◽  
pp. 89-101 ◽  
Author(s):  
H. J. A. Likuski ◽  
J. P. Bowland ◽  
R. T. Berg
Keyword(s):  
Lower Energy ◽  
Dry Matter ◽  
Energy Levels ◽  
Nitrogen Retention ◽  
Fine Aggregate ◽  
Protein Levels ◽  
Lower Energy Level ◽  
Lower Protein ◽  
Gross Energy ◽  
Old Rats

Diets containing gross energy levels of 3.9 and 3.2 Cal./gm. and crude protein levels of 14 and 18 per cent on an air-dry basis (4.4 and 3.5 Cal./gm and 15 and 20 per cent respectively on an oven-dry basis) were fed in a 2 × 2 factorial design to weanling rats and pigs. The lower energy level was achieved by adding 20 per cent of a fine aggregate of vermiculite. In the rat experiment the vermiculite was compared with a similar level or non-nutritive cellulose. Dry matter, apparent energy and apparent nitrogen digestibility and nitrogen retention were determined with 4- to 5-week-old rats weighing approximately 80 grams and with pigs averaging approximately 8, 20 and 50 kilograms liveweight.The apparent digestibility of energy and nitrogen by rats and pigs was similar. The percentage apparent nitrogen digestibility was reduced in both species fed lower energy diets. Dry matter and energy digestibilities were lowered in rats fed lower energy diets containing vermiculite but a similar effect was evident only in 8-kilogram pigs.Nitrogen retention varied between the two species. Percentage gross or digestible nitrogen retention in rats was increased with higher energy and with lower protein diets. Retention of digested nitrogen in Pigs was reduced with higher energy compared to lower energy diets. Higher protein improved nitrogen retention in 8-kilogram pigs but lowered retention in heavier pigs.

Observable Many-Body Effects of the Two-Body Unobservable Potential

1972 ◽  
Vol 50 (14) ◽  
pp. 1614-1618 ◽  
Author(s):  
N. N. Wong ◽  
M. Razavy
Keyword(s):  
Perturbation Theory ◽  
Phase Shift ◽  
Nuclear Matter ◽  
Particle Scattering ◽  
Body System ◽  
Many Body ◽  
Many Body Effects ◽  
Transparent Potential ◽  
The Many

A two-body transparent potential, which produces no observable phase shift in two-particle scattering, is constructed explicitly. This potential is used to calculate the energy of infinite nuclear matter by applying the perturbation theory and its effects on the many-body system are investigated.

Review Lecture. Calculations of nuclear structure

1972 ◽  
Vol 326 (1565) ◽  
pp. 199-213 ◽  
Keyword(s):  
Field Theory ◽  
Nuclear Structure ◽  
Single Particle ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Nucleon Nucleon ◽  
Body System ◽  
Many Body ◽  
Nucleon Scattering ◽  
Body Interaction

The field theory of elementary particles has so far failed to predict the detailed form of the interaction between neutrons and protons (nucleons), but the nucleon-nucleon scattering experiments are now sufficiently complete that for most purposes the interaction may be taken as known. At the same time a wealth of data concerning energy levels, transition probabilities and so on is available for literally hundreds of nuclei. Such measurements reveal that nuclei have an extremely rich structure, with both single-particle and collective properties, illustrating almost every feature of a many-body system. It is the purpose of this talk to review the extent to which we are able to understand these properties on the basis of the known two-body interaction. It will be shown how some features may be understood quite readily while others still pose fascinating problems.

Effects of different protein and energy levels on the performance of growing and finishing turkeys in the tropics

1981 ◽  
Vol 97 (3) ◽  
pp. 629-632
Author(s):  
J. M. Olomu ◽  
S. A. Offiong ◽  
S. Abed
Keyword(s):  
Weight Gain ◽  
Energy Level ◽  
Feed Efficiency ◽  
Lower Energy ◽  
Energy Levels ◽  
Metabolizable Energy ◽  
Feed Consumption ◽  
Lower Energy Level ◽  
Similar Weight ◽  
The Tropics

SUMMARYThree experiments were conducted to assess the effects of different protein and energy levels on turkeys during the periods 12–16 weeks, 16–20 weeks and 20–24 weeks. Compared with 20 and 22% protein, 18% significantly depressed weight gain and feed efficiency during the 12–16 weeks period, while 14 and 16% protein, compared with 18%, significantly depressed weight gain and feed efficiency during the 16–20 weeks period but gave similar weight gain and feed efficiency as the 18% protein during the 20–24 weeks period.During all periods between 12 and 24 weeks, the two energy levels tested (11·72 and 12·56 MJ/kg) did not significantly affect weight gain and feed efficiency whereas feed consumption was significantly higher on the lower energy level.The present studies suggest that 20, 18 and 16% protein, all with metabolizable energy of 11·72 MJ/kg, may be recommended for turkeys aged 12–16 weeks, 16–20 weeks and 20–24 weeks respectively.

Theoretical considerations of the effects of the medium upon molecular energy levels

1960 ◽  
Vol 255 (1280) ◽  
pp. 69-72 ◽  
Keyword(s):  
Dielectric Constant ◽  
Solute Atom ◽  
Energy Levels ◽  
The Other ◽  
Effective Dielectric Constant ◽  
Many Body ◽  
Frequency Shifts ◽  
The Many ◽  
Theoretical Considerations ◽  
Very High

For several years attempts have been made to allow for the effect of a solvent upon the energy levels of a solute atom or molecule by treating it as a medium with an effective dielectric constant. The solute is normally placed (figure 31) at the centre of a spherical cavity. One obvious advantage of such a model is that it attempts right from the start to deal with the many-body character of the forces which operate at very high gas densities and in liquids. But, as recent work by Bellamy (this Discussion) shows, such a non-specific explanation for the frequency shifts in vibration spectra is inadequate. This is not surprising. Indeed, one of the first requirements is that we should be able to distinguish those situations in which an effective-dielectric-constant approach is likely to be valid from the other situations where it is not. The latter situations are far more numerous than the former.

scholarly journals Towards quantitative accuracy in first-principles transport calculations: The GW method applied to alkane/gold junctions

2011 ◽  
Vol 2 ◽  
pp. 746-754 ◽  
Author(s):  
Mikkel Strange ◽  
Kristian S Thygesen
Keyword(s):  
Dft Calculations ◽  
First Principles ◽  
Density Functional ◽  
Energy Levels ◽  
Many Body ◽  
Gw Approximation ◽  
Quantitative Accuracy ◽  
Dynamic Screening ◽  
Electronic Conductance ◽  
The Many

The calculation of the electronic conductance of nanoscale junctions from first principles is a long-standing problem in the field of charge transport. Here we demonstrate excellent agreement with experiments for the transport properties of the gold/alkanediamine benchmark system when electron–electron interactions are described by the many-body GW approximation. The conductance follows an exponential length dependence: G n = G c exp(−βn). The main difference from standard density functional theory (DFT) calculations is a significant reduction of the contact conductance, G c , due to an improved alignment of the molecular energy levels with the metal Fermi energy. The molecular orbitals involved in the tunneling process comprise states delocalized over the carbon backbone and states localized on the amine end groups. We find that dynamic screening effects renormalize the two types of states in qualitatively different ways when the molecule is inserted in the junction. Consequently, the GW transport results cannot be mimicked by DFT calculations employing a simple scissors operator.

scholarly journals INFORMATION ON THE SIZE AND OTHER QUANTITIES OF Λ-ORBITALS IN HYPERNUCLEI FROM EXPERIMENTAL Λ-ENERGIES

2019 ◽  
Vol 11 ◽  
Author(s):  
M. E. Grypeos ◽  
C. G. Koutroulos ◽  
Th. A. Petridou
Keyword(s):  
Kinetic Energy ◽  
Wide Class ◽  
Ground State ◽  
Lower Energy ◽  
Energy Levels ◽  
Mean Square ◽  
Direct Information ◽  
Central Potential ◽  
Energy Eigenvalues

An approach is proposed on the basis of which the experimentally known two lower energy eigenvalues of a Λ- particle assumed to be bound in a hypernucleus by a central potential (from a fairly wide class of them) are able to provide in certain cases rather direct information on estimates of other useful quantities, such as the r.m.s. radii of the Λ Orbitals, kinetic energies, etc. In addition two basic inequalities relating the ground-state mean square radius of the orbit of a particle in a central potential and its kinetic energy, respectively, to the spacing of the two lowest energy levels ΔΕ are investigated and further discussed in connection with the Λ-hypernuclei.

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