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F Skiff - One of the best experts on this subject based on the ideXlab platform.
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complete Spectrum of kinetic eigenmodes for plasma oscillations in a weakly collisional plasma
Physical Review Letters, 2004Co-Authors: A Bhattacharjee, F SkiffAbstract:Kinetic eigenmodes of plasma oscillations in a weakly collisional plasma, described by a collision operator of the Fokker-Planck type, are obtained in closed form for initial-value as well as for boundary-value problems. These eigenmodes, which are smooth and compose a complete Discrete Spectrum, play the same role for weakly collisional plasmas as the Case-Van Kampen modes do for collisionless plasmas.
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kinetic eigenmodes and Discrete Spectrum of plasma oscillations in a weakly collisional plasma
Physical Review Letters, 1999Co-Authors: A Bhattacharjee, F SkiffAbstract:The damping of plasma oscillations in a weakly collisional plasma is revisited using a Fokker-Planck collision operator. It is shown that the Case--Van Kampen continuous Spectrum is eliminated in the limit of zero collision frequency and replaced by a Discrete Spectrum. The Landau-damped solutions are recovered in this limit, but as true eigenmodes of the weakly collisional system. For small but nonzero collision frequency, the spectra and eigenmodes are qualitatively different from their counterparts in the collisionless theory. These results are consistent with recent experimental findings.
A Bhattacharjee - One of the best experts on this subject based on the ideXlab platform.
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complete Spectrum of kinetic eigenmodes for plasma oscillations in a weakly collisional plasma
Physical Review Letters, 2004Co-Authors: A Bhattacharjee, F SkiffAbstract:Kinetic eigenmodes of plasma oscillations in a weakly collisional plasma, described by a collision operator of the Fokker-Planck type, are obtained in closed form for initial-value as well as for boundary-value problems. These eigenmodes, which are smooth and compose a complete Discrete Spectrum, play the same role for weakly collisional plasmas as the Case-Van Kampen modes do for collisionless plasmas.
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kinetic eigenmodes and Discrete Spectrum of plasma oscillations in a weakly collisional plasma
Physical Review Letters, 1999Co-Authors: A Bhattacharjee, F SkiffAbstract:The damping of plasma oscillations in a weakly collisional plasma is revisited using a Fokker-Planck collision operator. It is shown that the Case--Van Kampen continuous Spectrum is eliminated in the limit of zero collision frequency and replaced by a Discrete Spectrum. The Landau-damped solutions are recovered in this limit, but as true eigenmodes of the weakly collisional system. For small but nonzero collision frequency, the spectra and eigenmodes are qualitatively different from their counterparts in the collisionless theory. These results are consistent with recent experimental findings.
Sergio Albeverio - One of the best experts on this subject based on the ideXlab platform.
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the Discrete Spectrum of the spinless one dimensional salpeter hamiltonian perturbed by δ interactions
Journal of Physics A, 2015Co-Authors: Sergio Albeverio, S Fassari, F RinaldiAbstract:We rigorously define the self-adjoint one-dimensional Salpeter Hamiltonian perturbed by an attractive of strength centred at the origin, by explicitly providing its resolvent. Our approach is based on a ‘coupling constant renormalization’, a technique used first heuristically in quantum field theory and implemented in the rigorous mathematical construction of the self-adjoint operator representing the negative Laplacian perturbed by the in two and three dimensions. We show that the Spectrum of the self-adjoint operator consists of the absolutely continuous Spectrum of the free Salpeter Hamiltonian and an eigenvalue given by a smooth function of the parameter The method is extended to the model with two twin attractive deltas symmetrically situated with respect to the origin in order to show that the Discrete Spectrum of the related self-adjoint Hamiltonian consists of two eigenvalues, namely the ground state energy and that of the excited antisymmetric state. We investigate in detail the dependence of these two eigenvalues on the two parameters of the model, that is to say both the aforementioned strength and the separation distance. With regard to the latter, a remarkable phenomenon is observed: differently from the well-behaved Schrodinger case, the 1D-Salpeter Hamiltonian with two identical Dirac distributions symmetrically situated with respect to the origin does not converge, as the separation distance shrinks to zero, to the one with a single centred at the origin having twice the strength. However, the expected behaviour in the limit (in the norm resolvent sense) can be achieved by making the coupling of the twin deltas suitably dependent on the separation distance itself.
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On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics
Journal of Statistical Physics, 2007Co-Authors: Sergio Albeverio, Saidakhmat N Lakaev, Tulkin H RasulovAbstract:A model operator H associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles, is considered. The location of the essential Spectrum of H is described. The existence of infinitely many eigenvalues (resp. the finiteness of eigenvalues) below the bottom τ_ess( H ) of the essential Spectrum of H is proved for the case where the associated Friedrichs model has a threshold energy resonance (resp. a threshold eigenvalue). For the number N ( z ) of eigenvalues of H lying below z < τ_ess( H ) the following asymptotics is found $$\lim\limits_{z \to \tau_{\rm ess}(H)-0}\frac{N(z)}{|\log |z-\tau_{\rm ess}(H)||}={U}_0 (0
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on the Spectrum of an hamiltonian in fock space Discrete Spectrum asymptotics
arXiv: Mathematical Physics, 2005Co-Authors: Sergio Albeverio, Saidakhmat N Lakaev, Tulkin H RasulovAbstract:A model operator $H$ associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles, is considered. The precise location and structure of the essential Spectrum of $H$ is described. The existence of infinitely many eigenvalues below the bottom of the essential Spectrum of $H$ is proved for the case where an associated generalized Friedrichs model has a resonance at the bottom of its essential Spectrum. An asymptotics for the number $N(z)$ of eigenvalues below the bottom of the essential Spectrum is also established. The finiteness of eigenvalues of $H$ below the bottom of the essential Spectrum is proved if the associated generalized Friedrichs model has an eigenvalue with energy at the bottom of its essential Spectrum.
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schrodinger operators on lattices the efimov effect and Discrete Spectrum asymptotics
Annales Henri Poincaré, 2004Co-Authors: Sergio Albeverio, Saidakhmat N Lakaev, Zahriddin MuminovAbstract:The Hamiltonian of a system of three quantum mechanical particles moving on the three-dimensional lattice $$ \mathbb{Z}^3 $$ and interacting via zero-range attractive potentials is considered. For the two-particle energy operator h(k), with $$ k \in \mathbb{T}^3 = (-\pi, \pi]^3 $$ the two-particle quasi-momentum, the existence of a unique positive eigenvalue below the bottom of the continuous Spectrum of h(k) for k ≠ 0 is proven, provided that h(0) has a zero energy resonance. The location of the essential and Discrete spectra of the three-particle Discrete Schrodinger operator H(K), $$ k \in \mathbb{T}^3 $$ being the three-particle quasi-momentum, is studied. The existence of infinitely many eigenvalues of H(0) is proven. It is found that for the number N(0, z) of eigenvalues of H(0) lying below $$ z < 0 $$ the following limit exists $$ \lim_{z \to 0-}\, {N(0, z)\over |\log|z\|} = {\mathcal U}_0 $$ with $$ {\mathcal U}_0 > 0. $$ Moreover, for all sufficiently small nonzero values of the three-particle quasi-momentum K the finiteness of the number $$ N(K, \tau_{ess}(K))$$ of eigenvalues of H(K) below the essential Spectrum is established and the asymptotics for the number N(K, 0) of eigenvalues lying below zero is given.
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schr o dinger operators on lattices the efimov effect and Discrete Spectrum asymptotics
arXiv: Mathematical Physics, 2003Co-Authors: Sergio Albeverio, Saidakhmat N Lakaev, Zahriddin MuminovAbstract:The Hamiltonian of a system of three quantum mechanical particles moving on the three-dimensional lattice $\Z^3$ and interacting via zero-range attractive potentials is considered. For the two-particle energy operator $h(k),$ with $k\in \T^3=(-\pi,\pi]^3$ the two-particle quasi-momentum, the existence of a unique positive eigenvalue below the bottom of the continuous Spectrum of $h(k)$ for $k\neq0$ is proven, provided that $h(0)$ has a zero energy resonance. The location of the essential and Discrete spectra of the three-particle Discrete Schr\"{o}dinger operator $H(K), K\in \T^3$ being the three-particle quasi-momentum, is studied. The existence of infinitely many eigenvalues of H(0) is proven. It is found that for the number $N(0,z)$ of eigenvalues of H(0) lying below $z 0$. Moreover, for all sufficiently small nonzero values of the three-particle quasi-momentum $K$ the finiteness of the number $ N(K,\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the essential Spectrum is established and the asymptotics for the number $N(K,0)$ of eigenvalues lying below zero is given.
Feng Li Lin - One of the best experts on this subject based on the ideXlab platform.
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star spectroscopy in the constant b field background
Nuclear Physics, 2002Co-Authors: Bin Chen, Feng Li LinAbstract:Abstract In this paper we calculate the Spectrum of Neumann matrix with zero modes in the presence of the constant B -field in Witten's cubic string field theory. We find both the continuous Spectrum inside [−1/3,0) and the constraint on the existence of the Discrete Spectrum. For generic θ , −1/3 is not in the Discrete Spectrum but in the continuous Spectrum. For each eigenvalue in the continuous Spectrum there are four twist-definite degenerate eigenvectors except for −1/3 at which the degeneracy is two. However, for each twist-definite eigenvector the twist parity is opposite among the two spacetime components. Based upon the result at −1/3 we prove that the ratio of brane tension to be one as expected. Furthermore, we discuss the factorization of star algebra in the presence of B -field under the zero-slope limit and comment on the implications of our results to the recent proposed map of Witten's star to Moyal's star.
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star spectroscopy in the constant b field background
arXiv: High Energy Physics - Theory, 2002Co-Authors: Bin Chen, Feng Li LinAbstract:In this paper we calculate the Spectrum of Neumann matrix with zero modes in the presence of the constant B field in Witten's cubic string field theory. We find both the continuous Spectrum inside $[{-1\over3}, 0)$ and the constraint on the existence of the Discrete Spectrum. For generic $\theta$, -1/3 is not in the Discrete Spectrum but in the continuous Spectrum. For each eigenvalue in the continuous Spectrum there are four twist-definite degenerate eigenvector except for -1/3 at which the degeneracy is two. However, for each twist-definite eigenvector the twist parity is opposite among the two spacetime components. Based upon the result at -1/3 we prove that the ratio of brane tension to be one as expected. Furthermore, we discuss the factorization of star algebra in the presence of B field under zero-slope limit and comment on the implications of our results to the recent proposed map of Witten's star to Moyal's star.
Harald Woracek - One of the best experts on this subject based on the ideXlab platform.
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Canonical systems with Discrete Spectrum
Journal of Functional Analysis, 2020Co-Authors: Roman Romanov, Harald WoracekAbstract:Abstract We study spectral properties of two-dimensional canonical systems y ′ ( t ) = z J H ( t ) y ( t ) , t ∈ [ a , b ) , where the Hamiltonian H is locally integrable on [ a , b ) , positive semidefinite, and Weyl's limit point case takes place at b. We answer the following questions explicitly in terms of H: Is the Spectrum of the associated selfadjoint operator Discrete? If it is Discrete, what is its asymptotic distribution? Here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast. Making an analogy with complex analysis, this corresponds to convergence class and type w.r.t. proximate orders having order larger than 1. It is a surprising fact that these properties depend only on the diagonal entries of H. In 1968 L.de Branges posed the following question as a fundamental problem: Which Hamiltonians are the structure Hamiltonian of some de Branges space? We give a complete and explicit answer.
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Canonical systems with Discrete Spectrum
arXiv: Spectral Theory, 2019Co-Authors: Roman Romanov, Harald WoracekAbstract:We study spectral properties of two-dimensional canonical systems $y'(t)=zJH(t)y(t)$, $t\in[a,b)$, where the Hamiltonian $H$ is locally integrable on $[a,b)$, positive semidefinite, and Weyl's limit point case takes place at $b$. We answer the following questions explicitly in terms of $H$: Is the Spectrum of the associated selfadjoint operator Discrete ? If it is Discrete, what is its asymptotic distribution ? Here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast. Making an analogy with complex analysis, this corresponds to convergence class and type w.r.t.\ proximate orders having order larger than $1$. It is a surprising fact that these properties depend only on the diagonal entries of $H$. In 1968 this http URL~Branges posed the following question as a fundamental problem: Which Hamiltonians are the structure Hamiltonian of some\\ de~Branges space ? We give a complete and explicit answer.
