THE FINITENESS OF THE NUMBER OF EIGENVALUES OF THE FOUR-PARTICLE SCHRÖDINGER OPERATOR WITH THREE-PARTICLE CONTACT INTERACTION

2021 ◽  
Vol 10 (7) ◽  
pp. 2933-2946
Author(s):  
I. Bozorov ◽  
U. Shadiev ◽  
G. Yodgorov
Keyword(s):  
Essential Spectrum ◽  
Contact Interaction ◽  
Interaction Potential ◽  
Three Dimensional ◽  
Schrodinger Operator ◽  
Dimensional Lattice ◽  
Quasi Momentum ◽  
Particle Contact ◽  
Quantum Particles ◽  
Arbitrary Quantum

In this paper, we consider the four-particle Schr\"{o}dinger operator corresponding to the Hamiltonian of a system of four arbitrary quantum particles via a three-particle contact interaction potential on a three-dimensional lattice. The finiteness of the number of eigenvalues of the Schr\"{o}dinger operator lying to the left of the essential spectrum for zero value of the total quasi-momentum is proved.

scholarly journals The existence of eigenvalues of Schrödinger operator on a lattice in the gap of the essential spectrum

2021 ◽  
Vol 2070 (1) ◽  
pp. 012017
Author(s):  
J.I. Abdullaev ◽  
A.M. Khalkhuzhaev
Keyword(s):  
Essential Spectrum ◽  
Schrödinger Operator ◽  
Three Dimensional ◽  
Schrodinger Operator ◽  
Discrete Schrödinger Operator ◽  
Dimensional Lattice ◽  
Pairwise Potential ◽  
Zero Range

Abstract We consider a three-particle discrete Schrödinger operator Hμγ (K), K 2 T3 associated to a system of three particles (two fermions and one different particle) interacting through zero range pairwise potential μ > 0 on the three-dimensional lattice Z 3. It is proved that the operator Hμγ (K), ||K|| < δ, for γ > γ0 has at least two eigenvalues in the gap of the essential spectrum for sufficiently large μ > 0.

scholarly journals Bound states of a system of two bosons with a spherically potential on a lattice

2021 ◽  
Vol 2070 (1) ◽  
pp. 012023
Author(s):  
J.I. Abdullaev ◽  
Sh.H. Ergashova ◽  
Y.S. Shotemirov
Keyword(s):  
Invariant Subspace ◽  
Schrödinger Operator ◽  
Bound States ◽  
Three Dimensional ◽  
Invariant Subspaces ◽  
Bound State ◽  
Schrodinger Operator ◽  
Dimensional Lattice

Abstract We consider a Hamiltonian of a system of two bosons on a three-dimensional lattice Z 3 with a spherically simmetric potential. The corresponding Schrödinger operator H(k) this system has four invariant subspaces L(123), L(1), L(2) and L(3). The Hamiltonian of this system has a unique bound state over each invariant subspace L(1), L(2) and L(3). The corresponding energy values of these bound states are calculated exactly.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Flux tubes in three-dimensional lattice gauge theories

1993 ◽  
Vol 48 (5) ◽  
pp. 2290-2298 ◽  
Author(s):  
Howard D. Trottier ◽  
R. M. Woloshyn
Keyword(s):  
Gauge Theories ◽  
Three Dimensional ◽  
Flux Tubes ◽  
Dimensional Lattice ◽  
Lattice Gauge ◽  
Lattice Gauge Theories
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