scholarly journals Model of Quantum Chaotic Billiards: Spectral Statistics and Wave Functions in Two Dimensions

1996 ◽  
Vol 77 (10) ◽  
pp. 1970-1973 ◽  
Author(s):  
E. Cuevas ◽  
E. Louis ◽  
J. A. Vergés
Keyword(s):  
Two Dimensions ◽  
Wave Functions ◽  
Spectral Statistics ◽  
Chaotic Billiards

scholarly journals VARIATIONAL WAVE FUNCTIONS OF A VORTEX IN CYCLOTRON MOTION

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1601-1604 ◽  
Author(s):  
JIAN-MING TANG
Keyword(s):  
Uniform Magnetic Field ◽  
Energy Levels ◽  
Microscopic Theory ◽  
Two Dimensions ◽  
Wave Functions ◽  
Landau Levels ◽  
Cyclotron Motion ◽  
Rotational States ◽  
Variational Wave Functions ◽  
Variational Wave

In two dimensions the microscopic theory, which provides a basis for the naive analogy between a quantized vortex in a superfluid and an electron in an uniform magnetic field, is presented. A one-to-one correspondence between the rotational states of a vortex in a cylinder and the cyclotron states of an electron in the central gauge is found. Like the Landau levels of an electron, the energy levels of a vortex are highly degenerate. However, the gap between two adjacent energy levels does not only depend on the quantized circulation, but also increases with the energy, and scales with the size of the vortex.

scholarly journals Spheroidal wave-functions

1925 ◽  
Vol 107 (741) ◽  
pp. 43-60
Keyword(s):  
Wave Motion ◽  
Wave Length ◽  
Two Dimensions ◽  
Wave Functions ◽  
External Region ◽  
Spheroidal Wave Functions ◽  
Oblate Spheroidal ◽  
Usual Manner ◽  
Fundamental Vector ◽  
Velocity Of Propagation

The solution of problems relating to vibrations, in connection with spheroids— or, in two dimensions, elliptic cylinders—has hitherto only been attempted in one manner. If the vibrations have a time factor for their fundamental vector, of the form ℯ ipt , the equation of wave motion becomes, if ø is the fundamental vector, (∇ 2 + k 2 ) ø = 0 where the wave-length is 2π/ k ,and if C is the velocity of propagation of the wave in the external region, k = p/c . When oblate spheroidal co-ordinates are used, defined in terms of Cartesians by x= a √ { (1 + μ 2 ) (1 + ζ 2 ) } cos ω, y = a √ {1 - μ 2 ) (1 + ζ 2 ) } sin ω, z = a μζ, this can be transformed, after the usual manner, to ∂/∂μ (1 - μ 2 ) ∂ø/∂μ + ∂/∂ζ (1+ζ 2 ) ∂ø/∂ζ + k 2 a 2 (μ 2 + ζ 2 ) ø = 0, (1) when there is symmetry round the axis of z .

scholarly journals Parent Hamiltonian reconstruction of Jastrow-Gutzwiller wavefunctions

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Xhek Turkeshi ◽  
Marcello Dalmonte
Keyword(s):  
Parameter Space ◽  
Two Dimensions ◽  
Quantum Spin ◽  
Wave Functions ◽  
Strongly Correlated ◽  
Spin Liquids ◽  
Experimental Realization ◽  
Energy Field ◽  
Quantum Spin Liquids ◽  
Quantum Spin Liquid

Variational wave functions have been a successful tool to investigate the properties of quantum spin liquids. Finding their parent Hamiltonians is of primary interest for the experimental realization of these strongly correlated phases, and for gathering additional insights on their stability. In this work, we systematically reconstruct approximate spin-chain parent Hamiltonians for Jastrow-Gutzwiller wave functions, which share several features with quantum spin liquid wave functions in two dimensions. Firstly, we determine the different phases encoded in the parameter space through their correlation functions and entanglement properties. Secondly, we apply a recently proposed entanglement-guided method to reconstruct parent Hamiltonians to these states, which constrains the search to operators describing relativistic low-energy field theories - as expected for deconfined phases of gauge theories relevant to quantum spin liquids. The quality of the results is discussed using different quantities and comparing to exactly known parent Hamiltonians at specific points in parameter space. Our findings provide guiding principles for experimental Hamiltonian engineering of this class of states.

AN ALGEBRAIC APPROACH TO A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL IN TWO DIMENSIONS

2005 ◽  
Vol 20 (24) ◽  
pp. 5663-5670 ◽  
Author(s):  
SHI-HAI DONG ◽  
GUO-HUA SUN ◽  
M. LOZADA-CASSOU
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Algebraic Approach ◽  
Two Dimensions ◽  
Wave Functions ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Radial Wave ◽  
Commutation Relations ◽  
The Matrix

The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU (1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and [Formula: see text] with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r→ir.

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