MACROSCOPIC BOUNDARIES AND THE WAVE FUNCTION OF THE UNIVERSE IN THE c=-2 MATRIX MODEL

1991 ◽  
Vol 06 (31) ◽  
pp. 2901-2908 ◽  
Author(s):  
JONATHAN D. EDWARDS ◽  
IGOR R. KLEBANOV
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Matrix Model ◽  
Ground State ◽  
Bessel Functions ◽  
Scalar Fields ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Genus Expansion ◽  
The Universe

Using a matrix model, we calculate sums over surfaces with macroscopic boundaries of fixed lengths in two-dimensional gravity coupled to a pair of anti-commuting scalar fields with c=-2. For n boundaries, the answer depends only on the sum of their lengths and is given explicitly in terms of Bessel functions to all orders of the genus expansion. For n=1, this defines the Hartle-Hawking ground state wave function of the universe, which is shown to satisfy the minisuperspace Wheeler–De Witt equation with a boundary condition imposed at small geometries.

Phase diagram of cuprate high-temperature superconductors based on the optimization Monte Carlo method

2020 ◽  
Vol 34 (19n20) ◽  
pp. 2040046
Author(s):  
T. Yanagisawa ◽  
M. Miyazaki ◽  
K. Yamaji
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Wave Function ◽  
High Temperature ◽  
Hubbard Model ◽  
Ground State ◽  
State Energy ◽  
High Temperature Superconductivity ◽  
Two Dimensional ◽  
Text Model

It is important to understand the phase diagram of electronic states in the CuO2 plane to clarify the mechanism of high-temperature superconductivity. We investigate the ground state of electronic models with strong correlation by employing the optimization variational Monte Carlo method. We consider the two-dimensional Hubbard model as well as the three-band [Formula: see text]–[Formula: see text] model. We use the improved wave function that takes account of inter-site electron correlation to go beyond the Gutzwiller wave function. The ground state energy is lowered considerably, which now gives the best estimate of the ground state energy for the two-dimensional Hubbard model. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We investigate the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion [Formula: see text], the band parameter [Formula: see text] and the electron density [Formula: see text] for the Hubbard model. We show phase diagrams that include superconducting and antiferromagnetic phases. We expect that high-temperature superconductivity occurs near the boundary between antiferromagnetic phase and superconducting one. Since the three-band [Formula: see text]–[Formula: see text] model contains many-band parameters, high-temperature superconductivity may be more likely to occur in the [Formula: see text]–[Formula: see text] model than in single-band models.

On the Vanishing of the Cosmological Vacuum Energy

1997 ◽  
Vol 12 (16) ◽  
pp. 1127-1130 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Vacuum Energy ◽  
Ground State Solution ◽  
Space Time ◽  
State Solution ◽  
Superstring Theory ◽  
The Universe

By demanding the existence of a globally invariant ground-state solution of the Wheeler–De Witt equation (Schrödinger equation) for the wave function of the Universe Ψ, obtained from the heterotic superstring theory, in the four-dimensional Friedmann space-time, we prove that the cosmological vacuum energy has to be zero.

scholarly journals A CONFORMAL FIELD THEORY DESCRIPTION OF THE PAIRED AND PARAFERMIONIC STATES IN THE QUANTUM HALL EFFECT

2000 ◽  
Vol 15 (27) ◽  
pp. 1679-1688 ◽  
Author(s):  
GERARDO CRISTOFANO ◽  
GIUSEPPE MAIELLA ◽  
VINCENZO MAROTTA
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Conformal Field Theory ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Quantum Hall ◽  
Scalar Fields ◽  
Neutral Component ◽  
Conformal Field ◽  
Twisted Boundary Conditions

We extend the construction of the effective conformal field theory for the Jain hierarchical fillings proposed in Ref. 1 to the description of a quantum Hall fluid at nonstandard fillings [Formula: see text]. The chiral primary fields are found by using a procedure which induces twisted boundary conditions on the m scalar fields; they appear as composite operators of a charged and neutral component. The neutral modes describe parafermions and contribute to the ground state wave function with a generalized Pfaffian term. Correlators of Ne electrons in the presence of quasi-hole excitations are explicitly given for m=2.

scholarly journals GRAVITY ON A FUZZY SPHERE

2004 ◽  
Vol 19 (03) ◽  
pp. 361-370 ◽  
Author(s):  
P. VALTANCOLI
Keyword(s):  
Matrix Model ◽  
Solution Space ◽  
Two Dimensional ◽  
Fuzzy Sphere ◽  
Gauge Transformations ◽  
The Matrix ◽  
Analogous Model ◽  
Dimensional Gravity ◽  
Noncommutative Gravity ◽  
Noncommutative Plane

We propose an action for gravity on a fuzzy sphere, based on a matrix model. We find striking similarities with an analogous model of two-dimensional gravity on a noncommutative plane, i.e. the solution space of both models is spanned by pure U(2) gauge transformations acting on the background solution of the matrix model, and there exist deformations of the classical diffeomorphisms which preserve the two-dimensional noncommutative gravity actions.

DYNAMICAL TIME VARIABLE IN COSMOLOGY

1988 ◽  
Vol 03 (04) ◽  
pp. 333-343
Author(s):  
TAKESHI FUKUYAMA ◽  
KIYOSHI KAMIMURA
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Time Variable ◽  
Gravity Theory ◽  
Two Dimensional ◽  
Maximum Radius ◽  
Dynamical Time ◽  
Dimensional Gravity ◽  
Time Variables ◽  
The Universe

Dynamical time variables are studied in two dimensional gravity theory. Dynamical time and space variables exchange their role at the maximum radius (amax) like a black hole at event horizon. Dynamical arrows of time are directed towards amax in both expanding and contracting phases. Both time flows cannot go beyond amax, and the universe becomes static at amax.

ON THE COSMOLOGICAL CONSTANT IN QUANTUM COSMOLOGY OF THE BRANS–DICKE THEORY

1998 ◽  
Vol 13 (17) ◽  
pp. 1333-1337 ◽  
Author(s):  
ZONG-HONG ZHU ◽  
YUAN-ZHONG ZHANG ◽  
XIANG-PING WU
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Gravitational Theory ◽  
Wkb Approximation ◽  
Expanding Universe ◽  
The Universe

We study the issue of the cosmological constant in quantum cosmology combined with the Brans–Dicke gravitational theory. Using the minisuperspace approximation, we build up the Wheeler–De Witt equation and then obtain the wave function of the universe by further assuming the WKB approximation under the boundary condition proposed by Vilenkin. It is shown that the amplitude of the resulting wave function, which represents an expanding universe, reaches its peaks if the cosmological constant vanishes.

scholarly journals MATRIX MODELS OF TWO-DIMENSIONAL GRAVITY AND DISCRETE TODA THEORY

1996 ◽  
Vol 11 (22) ◽  
pp. 1797-1806 ◽  
Author(s):  
MASATO HISAKADO ◽  
MIKI WADATI
Keyword(s):  
Discrete Time ◽  
Matrix Model ◽  
Scaling Limit ◽  
Toda Chain ◽  
Partition Functions ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Molecule Equation

Recursion relations for orthogonal polynomials, arising in the study of one-matrix model of two-dimensional gravity, are shown to be equivalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by τ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.

scholarly journals MATRIX MODELS AND NON-PERTURBATIVE STRING PROPAGATION IN TWO-DIMENSIONAL BLACK HOLE BACKGROUNDS

1993 ◽  
Vol 08 (14) ◽  
pp. 1331-1341 ◽  
Author(s):  
SUMIT R. DAS
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
String Theory ◽  
Matrix Models ◽  
Matrix Model ◽  
Asymptotic Region ◽  
Two Dimensional ◽  
White Hole ◽  
Dimensional Black Hole ◽  
String Propagation

We identify a quantity in the c = 1 matrix model which describes the wave function for physical scattering of a tachyon from a black hole of the two-dimensional critical string theory. At the semiclassical level this quantity corresponds to the usual picture of a wave coming in from infinity, part of which enters the black hole becoming singular at the singularity, while the rest is scattered back to infinity, with nothing emerging from the white hole. We find, however, that the exact non-perturbative wave function is non-singular at the singularity and appears to end up in the asymptotic region "behind" the singularity.

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