Spectral properties of the massless relativistic harmonic oscillator

József Lőrinczi, Jacek Małecki

Type: Article

Publication Date: 2012-08-11

Citations: 62

DOI: https://doi.org/10.1016/j.jde.2012.07.010

View

Locations

Journal of Differential Equations - View
arXiv (Cornell University) - View - PDF
Loughborough University Institutional Repository (Loughborough University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Spectral Properties of the Massless Relativistic Harmonic Oscillator	2010	József Lőrinczi Jacek Małecki
+	Spectral Analysis of Relativistic Operators	2010	Alexander Balinsky W. D. Evans
+ PDF Chat	Spectral asymptotics for nonselfadjoint harmonic oscillators	2018	Víctor Arnaiz Gabriel Rivière
+ PDF Chat	Spectral properties of the Dirac operator coupled with $$\delta $$-shell interactions	2022	Badreddine Benhellal
+	Spectral Fluctuation Properties of the Non-Hermitian Dirac Operator	2000	H. Markum Rainer Pullirsch T. Wetting
+	Spectral Analysis of Relativistic Operators	2010	A. A. Balinsky W. D. Evans
+	Spectral and phase space analysis of the linearized non-cutoff Kac collision operator	2011	Nicolás Lerner Yoshinori Morimoto Karel Pravda–Starov Chao-Jiang Xu
+	Spectral Analysis of Integro-Differential Equations Arising in Thermal Physics	2022	Е. В. Панкратова
+	Approximate linear dependence, scaling and operator convergence in the harmonic oscillator problem	1964	Jan Nordling J. S. Faulkner
+	Asymptotics of the eigenvalues of the rotating harmonic oscillator	1998	T. M. Dunster
+	Spectral analysis of integro-differential equations in Hilbert space and its applications	2014	В. В. Власов
+	Spectral analysis of the Dirac-Maxwell system	2007	格佐々木
+	書評 A. A. Balinsky and W. D. Evans : Spectral Analysis of Relativistic Operators	2012	登美男楳田
+	Mathematical Methods in Quantum Mechanics	2009	Gerald Teschl
+	Spectral properties of the Dirac equation in unbounded vector potentials	2011	R. Giachetti
+ PDF Chat	Asymptotic Behaviour of the Spectral Kernel and its Derivatives for the Case of a Dirac System	1975	B. M. Levitan I. Sargsjan
+	Spectral theory for magnetic Schrodinger operators and applications	2008	Bernard Helffer
+	Evaluation of the asymptotic form in the generalized harmonic oscillator equation	1991	文雄宍戸 F Shishido
+	Spectral Theory and its Applications	2013	Bernard Helffer
+	Spectral analysis of pseudodifferential operators	1975	Ricardo Weder

Cited by (53)

Action	Title	Year	Authors
+ PDF Chat	Spectral properties of the fractional Fokker-Planck operator for the Lévy flight in a harmonic potential	2014	Ralf Toenjes Igor M. Sokolov Eugene B. Postnikov
+ PDF Chat	Higher order eigenvalues for non-local Schrödinger operators	2017	Niels Jacob Feng‐Yu Wang
+	On a class of anharmonic oscillators II. General case	2022	Marianna Chatzakou Julio Delgado Michael Ruzhansky
+	Contractivity and ground state domination properties for non-local Schr\"odinger operators	2015	Kamil Kaleta Mateusz Kwaśnicki József Lőrinczi
+ PDF Chat	Typical long-time behavior of ground state-transformed jump processes	2019	Kamil Kaleta József Lőrinczi
+ PDF Chat	Transition in the decay rates of stationary distributions of Lévy motion in an energy landscape	2016	Kamil Kaleta József Lőrinczi
+ PDF Chat	Zero-Energy Bound State Decay for Non-local Schrödinger Operators	2019	Kamil Kaleta József Lőrinczi
+	Universal Constraints on the Location of Extrema of Eigenfunctions of Non-Local Schr\"odinger Operators	2017	Anup Biswas József Lőrinczi
+ PDF Chat	Spectral properties of the massless relativistic quartic oscillator	2017	Samuel O. Durugo József Lőrinczi
+	Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman–Kac semigroups for a class of Lévy processes	2015	Kamil Kaleta József Lőrinczi
+	Fractional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>P</mml:mi><mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>ϕ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-processes and Gibbs measures	2012	Kamil Kaleta József Lőrinczi
+ PDF Chat	Fall-Off of Eigenfunctions for Non-Local Schrödinger Operators with Decaying Potentials	2016	Kamil Kaleta József Lőrinczi
+ PDF Chat	Spin-boson model through a Poisson-driven stochastic process	2014	Masao Hirokawa Fumio Hiroshima József Lőrinczi
+	Periodic Solutions of Generalized Schr\"odinger Equations on Cayley Trees	2013	Fumio Hiroshima József Lőrinczi U. A. Rozikov
+ PDF Chat	The spectrum of non-local discrete Schrödinger operators with a δ-potential	2014	Fumio Hiroshima József Lőrinczi
+	Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators	2019	Anup Biswas József Lőrinczi
+ PDF Chat	Multifractal properties of sample paths of ground state-transformed jump processes	2019	József Lőrinczi Xiaochuan Yang
+ PDF Chat	Potentials for non-local Schrödinger operators with zero eigenvalues	2022	Giacomo Ascione József Lőrinczi
+ PDF Chat	Contractivity and ground state domination properties for non-local Schrödinger operators	2018	Kamil Kaleta Mateusz Kwaśnicki József Lőrinczi
+ PDF Chat	Bulk Behaviour of Ground States for Relativistic Schrödinger Operators with Compactly Supported Potentials	2023	Giacomo Ascione József Lőrinczi
+	Spectral and analytic properties of some non-local Schrödinger operators and related jump processes	2015	József Lőrinczi Kamil Kaleta Samuel O. Durugo
+	Spin-Boson Model through a Poisson-Driven Stochastic Process	2012	Masao Hirokawa Fumio Hiroshima József Lőrinczi
+	Analytic properties of fractional Schr\'odinger semigroups and Gibbs measures for symmetric stable processes	2010	Kamil Kaleta József Lőrinczi
+ PDF Chat	Extension technique for complete Bernstein functions of the Laplace operator	2018	Mateusz Kwaśnicki Jacek Mucha
+ PDF Chat	Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity	2017	Silvestro Fassari M. Gadella M. L. Glasser L. M. Nieto
+ PDF Chat	Spectral properties of the two-dimensional Schrödinger Hamiltonian with various solvable confinements in the presence of a central point perturbation	2019	Silvestro Fassari M. Gadella M. L. Glasser L. M. Nieto Fabio Rinaldi
+ PDF Chat	Almost-sure explosive solutions of some nonlinear parabolic Itô equations	2015	Pao–Liu Chow R. Z. Khas’minskiĭ
+	Decay of harmonic functions for discrete time Feynman–Kac operators with confining potentials	2022	Wojciech Cygan Kamil Kaleta Mateusz Śliwiński
+	Higher-order airy functions of the first kind and spectral properties of the massless relativistic quartic anharmonic oscillator	2014	Samuel O. Durugo
+ PDF Chat	The behaviour of the three-dimensional Hamiltonian -Δ+λ[δ(x+x0)+δ(x-x0)] as the distance between the two centres vanishes	2017	S. Albeverio Silvestro Fassari Fabio Rinaldi
+	$$L^p$$-$$L^q$$ Boundedness of Fourier Multipliers Associated with the Anharmonic Oscillator	2023	Marianna Chatzakou Vishvesh Kumar
+ PDF Chat	Nonlocally induced (fractional) bound states: Shape analysis in the infinite Cauchy well	2015	Mariusz Żaba Piotr Garbaczewski
+ PDF Chat	Rational Spectral Methods for PDEs Involving Fractional Laplacian in Unbounded Domains	2020	Tao Tang Li-Lian Wang Huifang Yuan Tao Tang
+	Higher Order Eigenvalues for Non-Local Schrödinger Operators	2017	Niels Jacob Feng‐Yu Wang
+ PDF Chat	Ultrarelativistic bound states in the spherical well	2016	Mariusz Żaba Piotr Garbaczewski
+	On a class of anharmonic oscillators	2021	Marianna Chatzakou Julio Delgado Michael Ruzhansky
+	Hermite spectral collocation methods for fractional PDEs in unbounded domains	2018	Tao Tang Huifang Yuan Tao Tang
+	Extension technique for complete Bernstein functions of the Laplace operator	2017	Mateusz Kwaśnicki Jacek Mucha
+	Threshold Analysis of the One-Rank Perturbation Non-Local Discrete Laplacian	2022	Sh. S. Lakaev O. I. Kurbonov V. U. Aktamova
+ PDF Chat	Killing (absorption) versus survival in random motion	2017	Piotr Garbaczewski

Citing (27)

Action	Title	Year	Authors
+	Bernstein Functions: Theory and Applications	2010	René L. Schilling Renming Song Zoran Vondraček
+	Airy Functions and Applications to Physics	2004	Olivier Vallée M.J. Soares
+	Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes	2006	Tadeusz Kulczycki Bartłomiej Siudeja
+	Analytic properties of fractional Schr\'odinger semigroups and Gibbs measures for symmetric stable processes	2010	Kamil Kaleta József Lőrinczi
+	Fractional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>P</mml:mi><mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>ϕ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-processes and Gibbs measures	2012	Kamil Kaleta József Lőrinczi
+	Feynman-Kac-Type Theorems and Gibbs Measures on Path Space: With Applications to Rigorous Quantum Field Theory	2011	József Lőrinczi Fumio Hiroshima Volker Betz
+	Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman–Kac semigroups for a class of Lévy processes	2015	Kamil Kaleta József Lőrinczi
+ PDF Chat	Relativistic Schrödinger operators: Asymptotic behavior of the eigenfunctions	1990	René Carmona Wen Chen Masters Barry Simon
+ PDF Chat	Heat kernel estimates for the Dirichlet fractional Laplacian	2010	Zhen-Qing Chen Panki Kim Renming Song
+	Inequalities for the Zeros of the Airy Functions	1991	Giovanna Pittaluga Laura Sacripante
+ PDF Chat	Maxima of sums of random variables and suprema of stable processes	1973	Ν. H. Bingham
+	Intrinsic Ultracontractivity and Conditional Gauge for Symmetric Stable Processes	1997	Zhen-Qing Chen Renming Song
+	On Bounds for the Normal Integral	1955	John T. Chu
+ PDF Chat	Bounds for zeros of some special functions	1970	Herbert W. Hethcote
+ PDF Chat	Fractional quantum mechanics	2000	Nick Laskin
+	Some solutions to the space fractional Schrödinger equation using momentum representation method	2007	Jianping Dong Mingyu Xu
+ PDF Chat	PATH INTEGRAL REPRESENTATION FOR SCHRÖDINGER OPERATORS WITH BERNSTEIN FUNCTIONS OF THE LAPLACIAN	2012	Fumio Hiroshima Takashi Ichinose József Lőrinczi
+ PDF Chat	Trace estimates for stable processes	2007	Rodrigo Bañuelos Tadeusz Kulczycki
+ PDF Chat	Intrinsic Ultracontractivity for Schrödinger Operators Based on Fractional Laplacians	2010	Kamil Kaleta Tadeusz Kulczycki
+	Feynman-Kac-Type Theorems and Gibbs Measures on Path Space	2011	József Lőrinczi Fumio Hiroshima Volker Betz
+	Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables	1965	D. B. Owen Milton Abramowitz Irene A. Stegun
+ PDF Chat	Lieb-Thirring bound for Schrödinger operators with Bernstein functions of the Laplacian	2012	Fumio Hiroshima József Lőrinczi
+	Eigenvalues of the fractional Laplace operator in the interval	2011	Mateusz Kwaśnicki
+	Heat Kernel Estimates for Dirichlet Fractional Laplacian	2009	Panki Kim Zhenqing Renming Song
+ PDF Chat	Heat kernel estimates for the fractional Laplacian with Dirichlet conditions	2010	Krzysztof Bogdan Tomasz Grzywny Michał Ryznar
+ PDF Chat	Spectral properties of the Cauchy process on half-line and interval	2010	Tadeusz Kulczycki Mateusz Kwaśnicki Jacek Małecki Andrzej Stós
+	Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables	1965	J. W. W. Milton Abramowitz Irene A. Stegun