Definition of the Riesz derivative and its application to space fractional quantum mechanics

Download

index.pdf

Date

2016-12-01

Author

Bayin, Selcuk S.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

212
views

0
downloads

We investigate and compare different representations of the Riesz derivative, which plays an important role in anomalous diffusion and space fractional quantum mechanics. In particular, we show that a certain representation of the Riesz derivative, Rax, that is generally given as also valid for alpha = 1, behaves no differently than the other definition given in terms of its Fourier transform. In the light of this, we discuss the alpha -> 1 limit of the space fractional quantum mechanics and its consistency. Published by AIP Publishing.

URI

https://hdl.handle.net/11511/63639

Journal

JOURNAL OF MATHEMATICAL PHYSICS

DOI

https://doi.org/10.1063/1.4968819

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Generalization of a theorem of Bohr for bases in spaces of holomorphic functions of several complex variables Aizenberg, L; Aytuna, A; Djakov, P (Elsevier BV, 2001-06-15) In the first part, we generalize the classical result of Bohr by proving that an analogous phenomenon occurs whenever D is an open domain in C-m (or, more generally, a complex manifold) and (phi (n))(n=0)(infinity) is a basis in the space of holomorphic functions H(D) such that phi (0) = 1 and phi (n)(z(0)) = 0, n greater than or equal to 1, for some z(0) is an element of D. Namely, then there exists a neighborhood U of the point to such that, whenever a holomorphic function on D has modulus less than 1, th...
Engineering nonlinear response of nanomaterials using Fano resonances Turkpence, Deniz; Akguc, Gursoy B.; Bek, Alpan; Taşgın, Mehmet Emre (IOP Publishing, 2014-10-01) We show that nonlinear optical processes of nanoparticles can be controlled by the presence of interactions with a molecule or a quantum dot. By choosing the appropriate level spacing for the quantum emitter, one can either suppress or enhance the nonlinear frequency conversion. We reveal the underlying mechanism for this effect, which is already observed in recent experiments: (i) suppression occurs simply because transparency induced by Fano resonance does not allow an excitation at the converted frequenc...
Effective theory of interacting fermions in shaken square optical lattices Keleş, Ahmet; Liu, W. Vincent (2017-06-01) We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in a circularly shaken square lattice with near-resonance frequencies, i.e., tuned close to the energy separation between the s band and the p bands. First, we derive a time-independent four-band effective Hamiltonian in the noninteracting limit. Diagonalization of the effective Hamiltonian yields a quasienerg...
Properties of excited B-c states in QCD Alıyev, Tahmasıb; Bilmiş, Selçuk (Elsevier BV, 2019-10-01) The mass and leptonic decay constants of recently observed two new excited B-c states at LHC are studied within the QCD sum rules. Considering the contributions of the ground and radially excited states, the mass and residues of the excited states of pseudoscalar and vector mesons are calculated in the framework of two different approaches of the QCD sum rules, namely, linear combinations of the corresponding sum rules and its derivatives as well as QCD sum rules with the incorporation of the least square f...
First law of black hole thermodynamics and Smarr formula with a cosmological constant Hajian, Kamal; Özşahin, Hikmet; Tekin, Bayram (2021-08-01) The first law of black hole thermodynamics in the presence of a cosmological constant Lambda can be generalized by introducing a term containing the variation delta Lambda. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge, etc., it has been shown [Classical Quant. Gray. 35, 125012 (2018)] that the new term has the same structure: Lambda is a conserved charge associated with a gauge symmetry; and its role in the firs...

Citation Formats

S. S. Bayin, “Definition of the Riesz derivative and its application to space fractional quantum mechanics,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63639.