scholarly journals T $$ \overline{T} $$ deformation in SCFTs and integrable supersymmetric theories

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Stephen Ebert ◽  
Hao-Yu Sun ◽  
Zhengdi Sun
Keyword(s):  
Ground State ◽  
State Energy ◽  
Burgers Equation ◽  
Elliptic Genus ◽  
Leading Order ◽  
Superconformal Field Theories ◽  
S Matrix ◽  
Witten Index ◽  
Supersymmetric Theories ◽  
Ground State Energies

Abstract We calculate the $$ \mathcal{S} $$ S -multiplets for two-dimensional Euclidean $$ \mathcal{N} $$ N = (0, 2) and $$ \mathcal{N} $$ N = (2, 2) superconformal field theories under the T$$ \overline{T} $$ T ¯ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $$ \mathcal{N} $$ N = (0, 2) deformed multiplets, we calculate two- and three-point correlators. We show the $$ \mathcal{N} $$ N = (0, 2) chiral ring’s elements do not flow under the T$$ \overline{T} $$ T ¯ deformation. Specializing to integrable supersymmetric seed theories, such as $$ \mathcal{N} $$ N = (2, 2) Landau-Ginzburg models, we use the thermodynamic Bethe ansatz to study the S-matrices and ground state energies. From both an S-matrix perspective and Melzer’s folding prescription, we show that the deformed ground state energy obeys the inviscid Burgers’ equation. Finally, we show that several indices independent of D-term perturbations including the Witten index, Cecotti-Fendley-Intriligator-Vafa index and elliptic genus do not flow under the T$$ \overline{T} $$ T ¯ deformation.

scholarly journals BOUNDARY ONE-POINT FUNCTIONS, SCATTERING, AND BACKGROUND VACUUM SOLUTIONS IN TODA THEORIES

2003 ◽  
Vol 18 (06) ◽  
pp. 879-899 ◽  
Author(s):  
V. A. FATEEV ◽  
E. ONOFRI
Keyword(s):  
Exact Solutions ◽  
Ground State ◽  
S Matrix ◽  
Parametric Families ◽  
Vacuum Solutions ◽  
Ground State Energies

The parametric families of integrable boundary affine Toda theories are considered. We calculate boundary one-point functions and propose boundary S-matrices in these theories. We use boundary one-point functions and S-matrix amplitudes to derive boundary ground state energies and exact solutions describing classical vacuum configurations.

On the formation of cavitylike small-polaronic states in solid deuterium

1985 ◽  
Vol 63 (1) ◽  
pp. 94-98 ◽  
Author(s):  
S. K. Bose ◽  
J. D. Poll
Keyword(s):  
Ground State ◽  
Continuum Model ◽  
State Energy ◽  
Stark Shift ◽  
Localized State ◽  
Solid Deuterium ◽  
Vibrational Levels ◽  
Radiation Induced ◽  
Absorption Features ◽  
Ground State Energies

Certain infrared absorption features in tritiated as well as proton-irradiated samples of solid deuterium have been attributed to the formation of bubblelike electronic states localized in the lattice. These bubblelike states are shown to be energetically stable in the Wigner–Seitz model of the crystal and the gap between the ground-state energies in the bubble and the quasi-free states of the electron is calculated. An initial trapping of the electron by a vacancy is assumed in calculating the localized state energy. Calculations based on a continuum model of the solid yield the radius of such bubbles to close agreement with that obtained from the observed Stark shift of the vibrational levels of the neighbouring molecules due to the localized electrons. The model is used to interpret the radiation-induced absorption in proton-irradiated solid deuterium in the spectral region 4000–7500 cm−1.

scholarly journals Remarks on the boundary set of spectral equipartitions

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120492 ◽  
Author(s):  
P. Bérard ◽  
B. Helffer
Keyword(s):  
Riemannian Manifold ◽  
Lower Bound ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Two Dimensional ◽  
Nodal Sets ◽  
Nodal Domains ◽  
Open Set ◽  
Ground State Energies

Given a bounded open set in (or in a Riemannian manifold), and a partition of Ω by k open sets ω j , we consider the quantity , where λ ( ω j ) is the ground state energy of the Dirichlet realization of the Laplacian in ω j . We denote by ℒ k ( Ω ) the infimum of over all k -partitions. A minimal k -partition is a partition that realizes the infimum. Although the analysis of minimal k -partitions is rather standard when k =2 (we find the nodal domains of a second eigenfunction), the analysis for higher values of k becomes non-trivial and quite interesting. Minimal partitions are in particular spectral equipartitions, i.e. the ground state energies λ ( ω j ) are all equal. The purpose of this paper is to revisit various properties of nodal sets, and to explore if they are also true for minimal partitions, or more generally for spectral equipartitions. We prove a lower bound for the length of the boundary set of a partition in the two-dimensional situation. We consider estimates involving the cardinality of the partition.

scholarly journals MASSLESS FLOWS II: THE EXACT S-MATRIX APPROACH

1993 ◽  
Vol 08 (32) ◽  
pp. 5751-5778 ◽  
Author(s):  
P. FENDLEY ◽  
H. SALEUR ◽  
AL. B. ZAMOLODCHIKOV
Keyword(s):  
Magnetic Field ◽  
Ground State ◽  
State Energy ◽  
Casimir Energy ◽  
Matrix Approach ◽  
Minimal Models ◽  
Unusual Behavior ◽  
Conformal Field ◽  
S Matrix ◽  
Sine Gordon Model

We study the spectrum, the massless S matrices and the ground-state energy of the flows between successive minimal models of conformal field theory, and within the sine-Gordon model with imaginary coefficient of the cosine term (related to the minimal models by “truncation”). For the minimal models, we find exact S matrices which describe the scattering of massless kinks, and show using the thermodynamic Bethe ansatz that the resulting non-perturbative c function (defined by the Casimir energy on a cylinder) flows appropriately between the two theories, as conjectured earlier. For the nonunitary sine-Gordon model, we find unusual behavior. For the range of couplings we can study analytically, the natural S matrix deduced from the minimal one by “undoing” the quantum-group truncation does not reproduce the proper c function with the TBA. It does, however, describe the correct properties of the model in a magnetic field.

GROUND STATE ENERGIES OF HYDROGEN-LIKE IMPURITY IN A LENS-SHAPED QD

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2529-2533 ◽  
Author(s):  
XIANGHUA ZENG ◽  
JIAFENG CHANG ◽  
PENGXIA ZHOU
Keyword(s):  
Magnetic Field ◽  
Quantum Dot ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Lateral Deviation ◽  
Mass Approximation ◽  
The Magnetic Field ◽  
Ground State Energies ◽  
Electronic Ground

In this paper,the ground state energies of hydrogen-like impurity in a lens-shaped quantum dot ( GaAs / In 1-x Ga x As ) under vertical magnetic field have been discussed by using effective mass approximation and variational method. It gives that for a lens-shaped quantum dot, due to the asymmetry of the vertical and lateral bound potentials, the electronic ground state energies are related not only with the deviation distance but also with the deviation direction; for the spherical quantum dot, the ground state energy is only related with the distance of the impurity deviation, neither with vertical nor lateral deviation. And with the increasing of the magnetic field, the ground state energy is increasing.

INVESTIGATION OF NON-MAGNETIC AND FERROMAGNETIC PHASES OF 3D ELECTRON CRYSTAL WITH NaCl AND CsCl STRUCTURES

2008 ◽  
Vol 22 (21) ◽  
pp. 3627-3640
Author(s):  
R. RAJESWARA PALANICHAMY ◽  
M. ANANDAJOTHI ◽  
A. JAWAHAR ◽  
K. IYAKUTTI
Keyword(s):  
Ground State ◽  
State Energy ◽  
Correlation Energy ◽  
Magnetic Phase ◽  
Ferromagnetic Phase ◽  
Density Region ◽  
Wannier Functions ◽  
Ground State Energies ◽  
Electron Crystal

The non-magnetic and ferromagnetic phases of 3D Wigner electron crystal are investigated using a localized representation of the electrons with NaCl and CsCl structures. The ground state energies of ferromagnetic and non-magnetic phases of Wigner electron crystal are computed in the range 10 ≤ rs ≥ 130. The role of correlation energy is suitably taken into account. The low density region favorable for the ferromagnetic phase is found to be 4.8 × 1020 electrons/cm3 and for the non-magnetic phase, it is 2.03 × 1020 electrons/cm3. It is found that the ground state energy of ferromagnetic phase is less than that of the non-magnetic phase of the Wigner electron crystal. The structure-dependent Wannier functions, which give proper localized representation for Wigner electrons, are employed in the calculation.

scholarly journals On 1/Z expansion, the critical charge for a two-electron system, and the Kato theorem

2016 ◽  
Vol 94 (3) ◽  
pp. 249-253 ◽  
Author(s):  
A.V. Turbiner ◽  
J.C. Lopez Vieyra
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Critical Analysis ◽  
State Energy ◽  
Electron System ◽  
Chem Phys ◽  
Partial Sums ◽  
Consistency Check ◽  
Ground State Energies ◽  
Independent Confirmation

The 1/Z expansion for the ground state energy of the Coulomb system of an infinitely massive center of charge Z and two electrons (two-electron ionic sequence) is studied. A critical analysis of the 1/Z coefficients presented in Baker et al. (Phys. Rev. A, 41, 1247 (1990)) is performed and its numerical deficiency is indicated, leading, in particular, to unreliable decimal digits beyond digits 11–12 of the first coefficients. We made a consistency check of the 1/Z-expansion with accurate energies for Z = 1–10: the weighted partial sums of the 1/Z expansion with Baker et al. coefficients reproduce systematically the ground state energies of two-electron ions with Z ≥ 2 up to 12 decimal digits and for Z = 1 up to 10 decimal digits calculated by Nakashima and Nakatsuji (J. Chem. Phys. 127, 224104 (2007)) with unprecedented accuracy. This rules out the presence of non-analytic terms at Z = ∞ contributing to the first 10–12 decimal digits in the ground state energy; it agrees with the Kato theorem about convergence of the 1/Z expansion within that accuracy. The ground state energy of two-electron ions Z = 11 (Na9+) and Z = 12 (Mg10+) is calculated with 12 decimal digits. This study can be considered as the independent confirmation of the correctness of 10 decimal digits in all 401 coefficients of 1/Z-expansion printed in Baker et al. (Phys. Rev. A, 41, 1247 (1990)).

scholarly journals Quantum Mechanics and Nanotechnology

2021 ◽  
Author(s):  
Mulani Tabssum Tayyab
Keyword(s):  
Molecular Dynamics ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Quantum Physics ◽  
State Energy ◽  
Quantum Mechanical ◽  
Accurate Representation ◽  
Quantum Ground State ◽  
Ground State Energies

In quantum physics it is important that classical molecular dynamics studies of nanomachines may not give an accurate representation of their performance. Luckily another strategy, interior facilitate quantum Monte Carlo, a further developed method for processing quantum mechanical ground-state energies and wavefunctions, has the possible ability to demonstrate these frameworks. Some significant models show that the quantum ground state for some body frameworks like those of interest in nanotechnology has a subjectively unexpected construction in comparison to that got from a sub-atomic elements computation which displayed confusion and gross insecurities at energies of just a small amount of the ground-state energy. This outcome projects vulnerability on the unwavering quality of utilizing the sub-atomic elements strategy to ascertain the construction or some other dynamical amount pertinent to nanotechnology.

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