Fractional Quantum Mechanics and Levy Path Integrals

Abstract

The fractional quantum and statistical mechanics have been developed via new path integrals approach.

8 pages, added references for section 2

Cited by in corpus (165)

• Fractional Schrodinger equation
• Fractional Quantum Mechanics
• Fractional Schrödinger equation in optics
• Time fractional Schrodinger equation
• Ground state solutions for nonlinear fractional Schrödinger equations in ${\mathbb{R}}^N$
• Fractional dynamics of systems with long-range interaction
• Numerical Methods for Fractional Diffusion
• Fractional dynamics of coupled oscillators with long-range interaction
• Some properties of the one-dimensional Lévy crystal
• Nonlinear Fractional Dynamics on a Lattice with Long Range Interactions
• Experimental realisations of the fractional Schrödinger equation in the temporal domain
• Diffraction-free beams in fractional Schrödinger equation
• Numerical study of fractional Nonlinear Schrödinger equations
• Soliton dynamics in a fractional complex Ginzburg-Landau model
• One-dimensional solitons in fractional Schrödinger equation with a spatially modulated nonlinearity: nonlinear lattice
• Time Fractional Quantum Mechanics
• Fractional quantum mechanics in polariton condensates with velocity dependent mass
• Dynamics with Low-Level Fractionality
• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials
• Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics
• Symmetry breaking of spatial Kerr solitons in fractional dimension
• Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension
• Fractional Integrable Nonlinear Soliton Equations
• Stationary waves of Schrödinger-type equations with variable exponent
• Unveiling the link between fractional Schrödinger equation and light propagation in honeycomb lattice
• On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions
• Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities
• Ground states solutions for a non-linear equation involving a pseudo-relativistic Schrödinger operator
• Tunneling in Fractional Quantum Mechanics
• Fractional Derivative as Fractional Power of Derivative
• Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes
• Fractional Statistical Mechanics
• de Sitter Fractional Quantum Cosmology
• Sharp Threshold of Blow-up and Scattering for the fractional Hartree equation
• Nonholonomic Constraints with Fractional Derivatives
• Magnetohydrodynamics of Fractal Media
• Collocation method for fractional quantum mechanics
• Psi-Series Solution of Fractional Ginzburg-Landau Equation
• Quantum mechanics in fractional and other anomalous spacetimes
• Computing the ground and first excited states of the fractional Schrodinger equation in an infinite potential well
• Concentration phenomena for a fractional Schrödinger-Kirchhoff type equation
• Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems
• Quadratic fractional solitons
• On the Role of Information Theoretic Uncertainty Relations in Quantum Theory
• From Fractional Quantum Mechanics to Quantum Cosmology: An Overture
• Energy-dependent noncommutative quantum mechanics
• Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation
• Stable and oscillating solitons of $\mathcal{P}\mathcal{T}$-symmetric couplers with gain and loss in fractional dimension
• A unified meshfree pseudospectral method for solving both classical and fractional PDEs
• Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
• Concentration phenomena for a class of fractional Kirchhoff equations in ${\mathbb{R}}^N$ with general nonlinearities
• Inflation and fractional quantum cosmology
• Broadening quantum cosmology with a fractional whirl
• Existence and concentration of positive ground state solutions for nonlinear fractional Schrödinger-Poisson system with critical growth
• Numerical approximations for the tempered fractional Laplacian: Error analysis and applications
• Existence and concentration results for some fractional Schrödinger equations in ${\mathbb{R}}^N$ with magnetic fields
• Path Integral Formulation for Lévy Flights - Evaluation of the Propagator for Free, Linear and Harmonic Potentials in the Over- and Underdamped Limits
• The higher order fractional Calderón problem for linear local operators: uniqueness
• A high-order nodal discontinuous Galerkin method for nonlinear fractional Schrödinger type equations
• Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential
• Gauge Invariant Fractional Electromagnetic Fields
• Time independent fractional Schrodinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative
• Fractional Almost Kahler - Lagrange Geometry
• Fractional dark energy
• Fractional Laplacians in bounded domains: Killed, reflected, censored and taboo Lévy flights
• Estimated Age of the Universe in Fractional Cosmology
• Remarks on the inhomogeneous fractional nonlinear Schrodinger equation
• Fractional Holographic Dark Energy
• Conformal Anisotropic Mechanics
• Bubbles and W-shaped solitons in Kerr media with fractional diffraction
• Tunneling time in space fractional quantum mechanics
• Fractional Quantum Field Theory, Path Integral, and Stochastic Differential Equation for Strongly Interacting Many-Particle Systems
• Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers
• Sign-changing solutions for a class of zero mass nonlocal Schrödinger equations
• Global regularity of the three-dimensional fractional micropolar equations
• Strichartz estimates for the fractional Schrödinger and wave equations on compact manifolds without boundary
• Existence and multiplicity of solutions for fractional Schrödinger-Kirchhoff equations with Trudinger-Moser nonlinearity
• Fedosov Quantization of Fractional Lagrange Spaces
• Second-harmonic generation in the system with fractional diffraction
• One- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with fractional kinetic energy
• Multiplicity and concentration results for a fractional Schrödinger-Poisson type equation with magnetic field
• Zero mass case for a fractional Berestycki-Lions type problem
• Fractional Dirac Bracket and Quantization for Constrained Systems
• Localized modes in nonlinear fractional systems with deep lattices
• Domain walls in fractional media
• New scattering features in non-Hermitian space fractional quantum mechanics
• Factorization of the Quantum Fractional Oscillator
• Fractional Scalar Field Cosmology
• Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well
• A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time-space fractional diffusion equation
• Green function of the double fractional Fokker-Planck equation: Path integral and stochastic differential equations
• Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative
• Modified Friedmann equations from fractional entropy
• Multiplicity and concentration results for fractional Schrödinger-Poisson equations with magnetic fields and critical growth
• Existence and multiplicity of positive solutions for fractional Laplacian systems with nonlinear coupling
• Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions
• Ground state solutions for a fractional Schrödinger equation with critical growth
• Applications of density matrix in the fractional quantum mechanics
• Super Periodic Potential
• Kato smoothing, Strichartz and uniform Sobolev estimates for fractional operators with sharp Hardy potentials
• Multiple and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent
• Multiplicity and concentration of solutions for a fractional Kirchhoff equation with magnetic field and critical growth
• Concentrating solutions for a fractional Kirchhoff equation with critical growth
• Multiple solutions for a class of nonhomogeneous fractional Schrödinger equations in ${\mathbb{R}}^N$
• Unitary evolution for a two-level quantum system in fractional-time scenario
• On instability of standing waves for the mass-supercritical fractional nonlinear Schrödinger equation
• Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schrödinger Equations
• On fractional Schrödinger equations with Hartree type nonlinearities
• On the Study of Chaos and Memory Effects in the Bonhoeffer-van der Pol Oscillator with a Non-Ideal Capacitor
• Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations
• On the fractional NLS equation and the effects of the potential well's topology
• Self-accelerating beam dynamics in the space fractional Schrödinger equation
• Concentrating bounded states for fractional Schrödinger-Poisson system involving critical Sobolev exponent
• Fractional Generalization of Kac Integral
• On symmetrizing the ultraspherical spectral method for self-adjoint problems
• Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one
• Refined probabilistic global well-posedness for the weakly dispersive NLS
• Solutions of the fractional Schrödinger equation with sign-changing nonlinearity
• The Fractional Schrodinger Equation with the Generalized Woods-Saxon Potential
• Multi-peak semiclassical bound states for Fractional Schrödinger Equations with fast decaying potentials
• An existence result for singular fractional Kirchhoff-Schrödinger-Poisson system
• Existence and multiplicity of solutions for a nonlinear Schrödinger equation with non-local regional diffusion
• Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms
• Solitons in Quasiperiodic Lattices with Fractional Diffraction
• On the $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity
• Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity
• The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearities
• Fractional quantum mechanics meets quantum gravity phenomenology
• Fractional Schrödinger Equation with Zero and Linear Potentials
• One-dimensional L{é}vy Quasicrystal
• The second hyperpolarizability of systems described by the space-fractional Schrodinger equation
• Two-dimensional fractional discrete NLS equations: dispersion relations, rogue waves, fundamental and vortex solitons
• The weakly coupled fractional one-dimensional Schrödinger operator with index $1<\alpha \le 2$
• Cwikel Estimates and Negative Eigenvalues of Schroedinger Operators on Noncommutative Tori
• Global in time Strichartz estimates for the fractional Schrödinger equations on asymptotically Euclidean manifolds
• Concentration phenomena for fractional magnetic NLS equations
• Violation of f-sum Rule with Generalized Kinetic Energy
• Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal
• On the discreet spectrum of fractional quantum hydrogen atom in two dimensions
• Saddle solutions for the fractional Choquard equation
• The Fractionary Schrödinger Equation, Green Functions and Ultradistributions
• Fractional Particle and Sigma Model
• On a Fractional Schrödinger equation in the presence of Harmonic potential
• The scattering of fractional Schrödinger operators with short range potentials
• Multiple solutions for a fractional Schrodinger equation with potentials
• Existence of infinitely many solutions for the fractional Schrödinger- Maxwell equations
• Infinitely many solutions for $p$-fractional Choquard type equations involving general nonlocal nonlinearities with critical growth via the concentration compactness method
• Degenerate fractional Kirchhoff-type system with magnetic fields and upper critical growth
• Existence of infinitely many solutions for a class of fractional Schrödinger equations in ${\mathbb{R}}^N$ with combined nonlinearities
• Uniqueness of ground states to fractional nonlinear elliptic equations with harmonic potential
• Anomalous Paths in Quantum Mechanical Path-Integrals
• Principle action for particles faster than light
• Static hyperpolarizability of space-fractional quantum systems
• Constraining fractionality using some observational tests
• Tunable Bands in 1D Fractional Quantum Media
• The fractional Schrödinger equation on compact manifolds: Global controllability results
• The effect of non-local derivative on Bose-Einstein condensation
• Existence and uniqueness of solutions in fractional Orlicz-Sobolev spaces for a nonlocal singular elliptic problem
• Generalised fractional Rabi problem
• On the existence of multiple normalized solutions for a class of fractional Choquard equations with mixed nonlinearities
• Dynamics of periodic fractional discrete NLS in the continuum limit
• On degenerate fractional Schrödinger-Kirchhoff-Poisson equations with upper critical nonlinearity and electromagnetic fields