scholarly journals Ground-state energy of a Richardson-Gaudin integrable BCS model

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Yibing Shen ◽  
Phillip Isaac ◽  
Jon Links
Keyword(s):  
Integral Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Continuum Limit ◽  
State Energy ◽  
Mean Field ◽  
Bcs Model ◽  
Energy Expression ◽  
The Continuum

We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.

Tuning the Continuum Ground State Energy ofNO22−by Water Molecules

2005 ◽  
Vol 94 (22) ◽  
Author(s):  
A. Svendsen ◽  
H. Bluhme ◽  
M. O. A. El Ghazaly ◽  
K. Seiersen ◽  
S. Brøndsted Nielsen ◽  
...  
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Water Molecules ◽  
The Continuum

On ℓp-Gaussian–Grothendieck Problem

2021 ◽  
Author(s):  
Wei-Kuo Chen ◽  
Arnab Sen
Keyword(s):  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Mean Field ◽  
Stability Estimates ◽  
Spin Glass Model ◽  
Maximum Value ◽  
Glass Model ◽  
Gaussian Orthogonal Ensemble

Abstract For $p\geq 1$ and $(g_{ij})_{1\leq i,j\leq n}$ being a matrix of i.i.d. standard Gaussian entries, we study the $n$-limit of the $\ell _p$-Gaussian–Grothendieck problem defined as $$\begin{align*} & \max\Bigl\{\sum_{i,j=1}^n g_{ij}x_ix_j: x\in \mathbb{R}^n,\sum_{i=1}^n |x_i|^p=1\Bigr\}. \end{align*}$$The case $p=2$ corresponds to the top eigenvalue of the Gaussian orthogonal ensemble; when $p=\infty $, the maximum value is essentially the ground state energy of the Sherrington–Kirkpatrick mean-field spin glass model and its limit can be expressed by the famous Parisi formula. In the present work, we focus on the cases $1\leq p<2$ and $2<p<\infty .$ For the former, we compute the limit of the $\ell _p$-Gaussian–Grothendieck problem and investigate the structure of the set of all near optimizers along with stability estimates. In the latter case, we show that this problem admits a Parisi-type variational representation and the corresponding optimizer is weakly delocalized in the sense that its entries vanish uniformly in a polynomial order of $n^{-1}$.

EXACT MANY BODY FERMI-BOSE TRANSMUTATION IN 2+1 DIMENSIONS

1992 ◽  
Vol 06 (22) ◽  
pp. 3543-3553
Author(s):  
D.M. GAITONDE ◽  
SUMATHI RAO
Keyword(s):  
Gauge Field ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Mean Field ◽  
Scalar Interaction ◽  
Many Body ◽  
Ground State Wavefunction ◽  
The Many ◽  
Chern Simons

We show that the low energy limit of relativistic fermions interacting with a statistical gauge field also includes a scalar interaction. When the Chern-Simons (CS) parameter µ=e2/2π and the scalar interaction is precisely that which is obtained through relativistic reduction, the many-body Hamiltonian can be solved exactly, directly in the fermion gauge, for the ground state energy which is zero and the ground state wavefunction which is gauge equivalent to one, characteristic of free bosons. Conversely, for N bosons interacting with a CS gauge field with µ=e2/2π, the mean-field ground state energy is πN2/m, which is characteristic of N free fermions.

Ground state energy, binding energy, and the impurity-specific heat of the Anderson–Holstein model

2015 ◽  
Vol 93 (10) ◽  
pp. 1024-1029 ◽  
Author(s):  
Ch. Narasimha Raju ◽  
Ashok Chatterjee
Keyword(s):  
Binding Energy ◽  
Specific Heat ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Electron Phonon Interaction ◽  
Holstein Model

A single-level Anderson–Holstein model is studied using the Lang–Firsov transformation followed by a zero-phonon averaging and a Green function method within the framework of a mean-field approximation. The ground state energy of the system, the binding energy between the impurity and conduction electrons, and the impurity–electron spectral function are calculated. The effect of the electron–phonon interaction on the local moment as well as on the specific heat of the impurity electron is explored in the anti-adiabatic regime.

scholarly journals Ground state energy of mixture of Bose gases

2019 ◽  
Vol 31 (02) ◽  
pp. 1950005 ◽  
Author(s):  
Alessandro Michelangeli ◽  
Phan Thành Nam ◽  
Alessandro Olgiati
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Mean Field ◽  
Energy Functional ◽  
Length Scale ◽  
Asymptotic Results ◽  
Total Particle ◽  
The Many ◽  
Trapped Bosons

We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number [Formula: see text] becomes large. In the dilute regime, when the interaction potentials have the length scale of order [Formula: see text], we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is [Formula: see text], we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

The Ground-State Energy of Anisotropie Spin-Spin Interaction in One-Dimensional Chain

1969 ◽  
Vol 24 (5) ◽  
pp. 762-767
Author(s):  
A. D. Jannussis
Keyword(s):  
Integral Equation ◽  
Method Of Moments ◽  
Ground State Energy ◽  
Ground State ◽  
Algebraic System ◽  
State Energy ◽  
Spin Interaction ◽  
Dimensional Chain ◽  
Linear Algebraic System ◽  
One Dimensional

Abstract In the present work the integral equation of Yang and Yang is studied by the method of moments. In general the solution of the integral equation is reducible to a linear algebraic system which can be solved only approximately. From the solution of the system the ground-state energy and the magnetization of the anisotropic spin-spin interaction in a one-dimensional chain is de­termined.

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