Unique Wave Function Research Articles

Revealing Dielectric Screening in Twisted Graphene Devices

Researchers have revealed dielectric screening in twisted double bilayer graphene, in which the screening length is possibly larger than that of ABA-stacked tetralayer graphene owing to the unique wave function in the stacking direction.

Quantization of the canonical tensor model and an exact wave function

Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints provides an algebraically consistent way of discretizing the Dirac algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt quantization of the canonical tensor model. Formally one can obtain wave functions of the "universe" by solving the partial differential equations representing the constraints. For the simplest non-trivial case, the unique wave function is exactly and globally obtained. Although this case is far from being realistic, the wave function is physically interesting; locality is favored, and there exists a locus of configurations with features of the beginning of the universe.

QUANTUM CANONICAL TENSOR MODEL AND AN EXACT WAVE FUNCTION

Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints has structure functions, and provides an algebraically consistent way of discretizing the Dirac first-class constraint algebra for general relativity. This paper successfully formulates the Wheeler–DeWitt scheme of quantization of the canonical tensor model; the ordering of operators in the constraints is determined without ambiguity by imposing Hermiticity and covariance on the constraints, and the commutation algebra of constraints takes essentially the same form as the classical Poisson algebra, i.e. is first-class. Thus one could consistently obtain, at least locally in the configuration space, wave functions of "universe" by solving the partial differential equations representing the constraints, i.e. the Wheeler–DeWitt equations for the quantum canonical tensor model. The unique wave function for the simplest nontrivial case is exactly and globally obtained. Although this case is far from being realistic, the wave function has a few physically interesting features; it shows that locality is favored, and that there exists a locus of configurations with features of beginning of universe.

The real solution to scalar field equation in 5D black string space

After the nontrivial quantum parameters Ω n and quantum potentials V n obtained in our previous research, the circumstance of a real scalar wave in the bulk is studied with the similar method of Brevik and Simonsen (Gen. Rel. Grav. 33:1839, 2001). The equation of a massless scalar field is solved numerically under the boundary conditions near the inner horizon r e and the outer horizon r c . Unlike the usual wave function Ψωl in 4D, quantum number n introduces a new functions Ψωl n , whose potentials are higher and wider with bigger n. Using the tangent approximation, a full boundary value problem about the Schrödinger-like equation is solved. With a convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients are obtained. If extra dimension does exist and is visible at the neighborhood of black holes, the unique wave function Ψωl n may say something to it.

A Discussion on the Einstein–Podolski–Rosen (EPR) Effect* in a Unique Wavefunction Quantum Mechanical Framework

A unique wavefunction, constructed according to the original Einstein–Podolski–Rosen (EPR) description, is used here to analyze the behavior of two equal non-interacting quantum systems: S(1) and S(2).The results show that the EPR paradox, which will be referred as EPR effect in this work, always appears in this theoretical context. When the expectation value of a Hermitian operator is sought, it can yield two different values, when measured on S(1) or S(2). However, the EPR effect disappears if the wavefunction is chosen symmetric or antisymmetric by interchanging the S(1) and S(2) coordinates. The same EPR effect appears when the expectation value of a state selector projection operator is computed on S(1) or S(2), but it disappears within a symmetric or antisymmetric EPR wavefunction form. On the other hand, the action of the selectors over the EPR wavefunction provide images on EPR system S(1) or S(2) which could be different, so the EPR effect persists except if, similarly as in the statistical case, a wavefunction constructed with a symmetric or antisymmetric superposition with respect the EPR system coordinates is used. Thus, with appropriate wavefunction choices, in statistical expectation value measures and non-statistical selector images as well, the EPR effect could not persist.

Dynamical initial conditions in quantum cosmology.

Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large volume, a unique wave function is predicted.

Quantum cosmology of openR x S2 x S1.

We examine the classical and quantum cosmology of a Kantowski-Sachs spacetime manifold with a topology openR\ifmmode\times\else\texttimes\fi{}${\mathit{S}}^{2}$\ifmmode\times\else\texttimes\fi{}${\mathit{S}}^{1}$ and a nonzero cosmological constant, within the framework of canonical quantum gravity. The classical trajectories are analyzed, and it is shown that the classical problem can be reduced to that of free particles. Both the Hartle-Hawking ``no-boundary'' proposal and the Vilenkin ``outgoing flux'' proposal are examined. First, the Hartle-Hawking proposal is generalized to canonical quantum gravity by imposing generic initial conditions on the solutions to the Wheeler-DeWitt equation at small scale factors. The resulting wave function has essentially the same leading exponential behavior as the semiclassical approximation to the ``no-boundary'' Euclidean functional integral in the nonoscillatory region. It is further shown, by calculating overlap integrals with semiclassical wave functions, that the wave function diverges too quickly in this region to be interpreted probabilistically. An analogue of the Baum-Hawking factor appears, and is interpreted as indicating that, given a small \ensuremath{\Lambda}, the wave function is highly peaked around a class of configurations in which the ${\mathit{S}}^{2}$ radius is R=[1/(2G${\mathrm{\ensuremath{\Lambda}}}^{1/2}$)]. These configurations are classically unstable. Second, given a complete set of solutions to the Wheeler-DeWitt equation, the outgoing flux proposal is found to be insufficient to select a unique wave function. A source is found for the Wheeler-DeWitt current of the above solutions. No analogue of the Baum-Hawking factor appears in the outgoing flux model.

On the Vilenkin boundary condition proposal in anisotropic universes

We show that the Vilenkin boundary condition proposal, as formulated in terms of the Klein-Gordon type current, does not specify a unique wave function in the vacuum minisuperspace models of the Kantowski-Sachs type and the locally rotationally symmetric Bianchi type III. The underlying reasons are directly in the classical dynamics of the models. We also discuss the suggestion of relating the Vilenkin proposal to a lorentzian path integral with the causal boundary condition advocated by Teitelboim.