IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sat, 19 Jun 2021 09:41:00 GMT2021-06-19T09:41:00Z10231A criterion for the reality of the spectrum of PT-symmetric Schrödinger operators with complex-valued periodic potentialshttp://hdl.handle.net/11585/63377Titolo: A criterion for the reality of the spectrum of PT-symmetric Schrödinger operators with complex-valued periodic potentials
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/633772008-01-01T00:00:00ZConvergent quantum normal forms, PT-symmetry and reality of the spectrumhttp://hdl.handle.net/11585/209223Titolo: Convergent quantum normal forms, PT-symmetry and reality of the spectrum
Abstract: A class of non-selfadjoint, PT-symmetric operators is identified similar to a selfadjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed through the method of the quantum normal form, whose convergence (uniform with respect to the Planck constant) is proved. Further consequences of the uniform convergence of the quantum normal form are the establishment of an exact quantization formula for the eigenvalues and the integrability of the classical hamiltonian corresponding to the given PT-symmetric operator.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11585/2092232013-01-01T00:00:00ZCPT-conserving Hamiltonians and their nonlinear supersymmerization using differential charge operators Chttp://hdl.handle.net/11585/9337Titolo: CPT-conserving Hamiltonians and their nonlinear supersymmerization using differential charge operators C
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11585/93372005-01-01T00:00:00ZMeccanica: A conference in honor of Sandro Graffi on the occasion of his 65th birthdayhttp://hdl.handle.net/11585/64891Titolo: Meccanica: A conference in honor of Sandro Graffi on the occasion of his 65th birthday
Abstract: Aula Absidale S. Lucia, Universita` di Bologna, August 27-10, 2008
Aim of the meeting:
While celebrating Sandro Graffi's exceptional career, this meeting will bring together a few of the leading contributors, from different generations, to the areas of mathematical physics where Sandro has been a driving force. The aim is to discuss traditional and novel directions of research.
http://meccanica.dm.unibo.it/
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/648912008-01-01T00:00:00ZAn existence criterion for the PT -symmetric phase transitionhttp://hdl.handle.net/11585/393976Titolo: An existence criterion for the PT -symmetric phase transition
Abstract: We consider on $L^2(\R)$ the Schroedinger operator family $H(g)$ with domain and action defined as follows
$$
D(H(g))=H^2(\R)\cap L^2_{2M}(\R); \quad H(g) u=\bigg(-\frac{d^2}{dx^2}+\frac{x^{2M}}{2M}-g\,\frac{x^{M-1}}{M-1}\bigg)u
$$
where $g\in\C$, $M=2,4,\ldots\;$. $H(g)$ is self-adjoint if $g\in\R$, while $H(ig)$ is $\PT$-symmetric. We prove that $H(ig)$ exhibits the so-called $\P\T$-symmetric phase transition. Namely, for each eigenvalue $E_n(ig)$ of $H(ig)$, $g\in\R$, there exist $R_1(n)>R(n)>0$ such that $E_n(ig)\in\R$ for $|g|<R(n)$ and turns into a pair of complex conjugate eigenvalues for $|g|>R_1(n)$.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3939762014-01-01T00:00:00ZFrom useful algorithms for slowly convergent series to physical predictions based on divergent perturbative expansions.http://hdl.handle.net/11585/54036Titolo: From useful algorithms for slowly convergent series to physical predictions based on divergent perturbative expansions.
Abstract: This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods
for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has hitherto not
received the attention it actually deserves. The unifying concept for convergence acceleration methods is that in many cases, one can
reach much faster convergence than by adding a particular series term by term. In some cases, it is even possible to use a divergent
input series, together with a suitable sequence transformation, for the construction of numerical methods that can be applied to the
calculation of special functions. This review both aims to provide some practical guidance as well as a groundwork for the study of
specialized literature. As a second topic, we review some recent developments in the field of Borel resummation, which is generally
recognized as one of the most versatile methods for the summation of factorially divergent (perturbation) series. Here, the focus is
on algorithms which make optimal use of all information contained in a finite set of perturbative coefficients. The unifying concept
for the various aspects of the Borel method investigated here is given by the singularities of the Borel transform, which introduce
ambiguities from a mathematical point of view and lead to different possible physical interpretations. The two most important cases
are: (i) the residues at the singularities correspond to the decay width of a resonance; and (ii) the presence of the singularities
indicates the existence of nonperturbative contributions which cannot be accounted for on the basis of a Borel resummation and
require generalizations toward resurgent expansions. Both of these cases are illustrated by examples.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11585/540362007-01-01T00:00:00ZReality and non-reality of the spectrum of PT -symmetric operators: Operator-theoretic criteriahttp://hdl.handle.net/11585/79331Titolo: Reality and non-reality of the spectrum of PT -symmetric operators: Operator-theoretic criteria
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11585/793312009-01-01T00:00:00ZPT symmetric non-selfadjoint
operators, diagonalizable and non-diagonalizable, with real discrete spectrumhttp://hdl.handle.net/11585/53958Titolo: PT symmetric non-selfadjoint
operators, diagonalizable and non-diagonalizable, with real discrete spectrum
Abstract: Consider the operator family
H(g):=H_0+igW.
H_0 is the quantum harmonic
oscillator with rational frequencies , W a P symmetric bounded potential, and g a real coupling
constant.
We show that if |g|< does not exceed an explicitly determined constant, the spectrum of H(g) is
real and discrete. Moreover we show that the ope-rator
H(g)=a*_1 a_1+a*_2a_2+ig a*_2a_1 has real discrete spectrum but is not diagonalizable.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11585/539582007-01-01T00:00:00ZAn analytic family of PT-symmetric Hamiltonians with real eigenvalueshttp://hdl.handle.net/11585/64568Titolo: An analytic family of PT-symmetric Hamiltonians with real eigenvalues
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11585/645682008-01-01T00:00:00ZQuadratic PT -symmetric operators with real spectrum and similarity to self-adjoint operatorshttp://hdl.handle.net/11585/132841Titolo: Quadratic PT -symmetric operators with real spectrum and similarity to self-adjoint operators
Abstract: It is established that a PT -symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental matrix has no Jordan blocks.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11585/1328412012-01-01T00:00:00Z