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Mostafazadeh, Ali

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Now showing 1 - 10 of 155
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    Time-dependent diffeomorphisms as quantum canonical transformations and the time-dependent harmonic oscillator
    (Iop Publishing Ltd, 1998) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a previously unknown class of exactly solvable time-dependent harmonic oscillators. The Caldirola-Kanai oscillator belongs to this class. For a general time-dependent harmonic oscillator, it is shown that choosing the dilatation parameter to satisfy the classical equation of motion, one obtains the solution of the Schrodinger equation. A simple generalization of this result leads to the reduction of the Schrodinger equation to a second-order ordinary differential equation whose special case is the auxiliary equation of the Lewis-Riesenfeld invariant theory. The time-evolution operator is expressed in terms of a positive red solution of this equation in a closed form, and the time-dependent position and momentum operators are calculated.
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    Propagation of electromagnetic waves in linear media and pseudo-hermiticity
    (EPL Association, European Physical Society, 2008) Loran, F.; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We express the electromagnetic field propagating in an arbitrary time-independent non-dispersive medium in terms of an operator that turns out to be pseudo-Hermitian for Hermitian dielectric and magnetic permeability tensors (epsilon) over left right arrow and (mu) over left right arrow. We exploit this property to determine the propagating field. In particular, we obtain an explicit expression for a planar field in an isotropic medium with (epsilon) over left right arrow = epsilon(1) over left right arrow and mu = mu(1) over left right arrow varying along the direction of the propagation. We also study the scattering of plane waves due to a localized inhomogeneity.
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    Z(n)-graded topological generalizations of supersymmetry and orthofermion algebra
    (Iop Publishing Ltd, 2003) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We review various generalizations of supersymmetry and discuss their relationship. in particular, we show how supersymmetry, parasupersymmetry, fractional supersymmetry, orthosupersymmetry, and the Z(n)-graded topological symmetries are related.
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    Statistical origin of pseudo-Hermitian supersymmetry and pseudo-hermitian fermions
    (Iop Publishing Ltd, 2004) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N = 2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-phermion or a boson-abnormal-phermion exchange symmetry. We further establish the physical equivalence (nonequivalence) of phermions (abnormal phermions) with ordinary fermions, describe the underlying Lie algebras and study multi-particle systems of abnormal phermions. The latter provides a certain bosonization of multifermion systems.
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    Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti- PT -symmetry
    (American Physical Society, 2023) Loran, Farhang; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We develop a fundamental transfer-matrix formulation of the scattering of electromagnetic (EM) waves that incorporates the contribution of the evanescent waves and applies to general stationary linear media which need not be isotropic, homogenous, or passive. Unlike the traditional transfer matrices whose definition involves slicing the medium, the fundamental transfer matrix is a linear operator acting in an infinite-dimensional function space. It is given in terms of the evolution operator for a nonunitary quantum system and has the benefit of allowing for analytic calculations. In this respect it is the only available alternative to the standard Green's-function approaches to EM scattering. We use it to offer an exact solution of the outstanding EM scattering problem for an arbitrary finite collection of possibly anisotropic nonmagnetic point scatterers lying on a plane. In particular, we provide a comprehensive treatment of doublets consisting of pairs of isotropic point scatterers and study their spectral singularities. We show that identical and PT-symmetric doublets do not admit spectral singularities and cannot function as a laser unless the real part of their permittivity equals that of the vacuum. This restriction does not apply to doublets displaying anti-PT-symmetry. We determine the lasing threshold for a generic anti-PT-symmetric doublet and show that it possesses a continuous lasing spectrum.
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    Hilbert space structures on the solution space of Klein-Gordon-type evolution equations
    (Iop Publishing Ltd, 2003) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon-type evolution equation. This involves dealing with the peculiarities of formulating a unitary quantum dynamics in a Hilbert space with a time-dependent inner product. We apply our general results to obtain possible Hilbert space structures on the solution space of the equation of motion for a classical simple harmonic oscillator, a free Klein-Gordon equation and the Wheeler-DeWitt equation for the FRW-massive-real-scalar-field models.
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    Physics of spectral singularities
    (Trends in Mathematics, 2015) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In particular, we give a simple definition of spectral singularities, provide a general introduction to spectral consequences of ��-symmetry (clarifying some of the controversies surrounding this subject), outline the main ideas and constructions used in the pseudo-Hermitian representation of quantum mechanics, and discuss how spectral singularities entered in the physics literature as obstructions to these constructions. We then review the transfer matrix formulation of scattering theory and the application of complex scattering potentials in optics. These allow us to elucidate the physical content of spectral singularities and describe their optical realizations. Finally, we survey some of the most important results obtained in the subject, drawing special attention to the remarkable fact that the condition of the existence of linear and nonlinear optical spectral singularities yield simple mathematical derivations of some of the basic results of laser physics, namely the laser threshold condition and the linear dependence of the laser output intensity on the gain coefficient.
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    On the dynamical invariants and the geometric phases for a general spin system in a changing magnetic field
    (Elsevier Science Bv, 2001) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We consider a class of general spin Hamiltonians of the form H-S(t) = H-0(t) + H ' (t), where H-0(t) and H ' (t) describe the dipole interaction of the spins with an arbitrary time-dependent magnetic field and the internal interaction of the spins, respectively. We show that if H ' (t) is rotationally invariant, then H-S(t) admits the same dynamical invariant as H-0(t). A direct application of this observation is a straightforward rederivation of the results of Yan et al. (Phys. Lett. A 251 (1999) 289, 259 (1999) 207) on the Heisenberg spin system in a changing magnetic field.
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    Explicit realization of pseudo-Hermitian and quasi-Hermitian quantum mechanics for two-level systems
    (TÜBİTAK , 2006) N/A; Department of Mathematics; N/A; Mostafazadeh, Ali; Özçelik, Seher; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 4231; N/A
    We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators η-, and η+-pseudo-Hermitian operators acting in ℂ2. The latter represent the physical observables of a model whose Hamiltonian and Hubert space are respectively H and ℂ2 endowed with the inner product defined by η+. Our calculations allows for a direct demonstration of the fact that the choice of an irreducible family of observables fixes the metric operator up to a multiplicative factor.
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    Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions
    (IOP Publishing Ltd, 2009) Mehri-Dehnavi, Hossein; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    A curious feature of complex scattering potentials nu(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete biorthonormal system consisting of the eigenfunctions of the Hamiltonian operator, i.e., - d(2)/dx(2) + nu(x), and its adjoint. We establish the equivalence of this description with the mathematicians' definition of spectral singularities for the potential nu(x) = z_delta(x+a)+ z(+)delta(x-a), where z(+/-) and a are respectively complex and real parameters and delta(x) is the Dirac delta function. We offer a through analysis of the spectral properties of this potential and determine the regions in the space of the coupling constants z(+/-) where it admits bound states and spectral singularities. In particular, we find an explicit bound on the size of certain regions in which the Hamiltonian is quasi-Hermitian and examine the consequences of imposing PT-symmetry.