arXiv subjects
Publications and source records attributed to F. Cannata.
Symmetry energy is a key quantity in the study of the equation of state of asymmetric nuclear matter. Heavy ion collisions at low and intermediate energies, performed at Laboratori Nazionali di Legnaro and Laboratori Nazionali del Sud, can be used to extract information on the symmetry energy coefficient Csym, which is currently poorly known but relevant both for astrophysics and for structure of exotic nuclei.
In the framework of perturbation theory the reality of the perturbed eigenvalues of a class of $\PT$symmetric Hamiltonians is proved using stability techniques. We apply this method to $\PT$symmetric unperturbed Hamiltonians perturbed by $\PT$symmetric additional interactions.
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with hermiticity, T invariance and PT invariance.
We consider QM with non-Hermitian quasi-diagonalizable Hamiltonians, i.e. the Hamiltonians having a number of Jordan cells in particular biorthogonal bases. The "self-orthogonality" phenomenon is clarified in terms of a correct spectral decomposition and it is shown that "self-orthogonal" states never jeopardize resolution of identity and thereby quantum averages of observables. The example of a complex potential leading to one Jordan cell in the Hamiltonian is constructed and its origin from level coalescence is elucidated. Some puzzles with zero-binorm bound states in continuous spectrum are unraveled with the help of a correct resolution of identity.
Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model is based on a classical complex Lagrangian of a scalar field. Specific symmetry properties analogous to PT in non-Hermitian quantum mechanics lead to purely real equation of motion.
Supersymmetrical intertwining relations of second order in derivatives allow to construct a two-dimensional quantum model with complex potential, for which {\it all} energy levels and bound state wave functions are obtained analytically. This model {\it is not amenable} to separation of variables, and it can be considered as a specific complexified version of generalized two-dimensional Morse model with additional $\sinh^{-2}$ term. The energy spectrum of the model is proved to be purely real. To our knowledge, this is a rather rare example of a nontrivial exactly solvable model in two dimensions. The symmetry operator is found, the biorthogonal basis is described, and the pseudo-Hermiticity of the model is demonstrated. The obtained wave functions are found to be common eigenfunctions both of the Hamiltonian and of the symmetry operator.
A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part of the spectrum and corresponding wave functions, starting from {\it one} definite state, which can be obtained by the method of $SUSY$-separation of variables, proposed recently.
A brief overview is given of recent developments and fresh ideas at the intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). We study the consequences of the assumption that the "charge" operator C is represented in a differential-operator form. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. The integrability of intertwining relations proves to match the closure of nonlinear SUSY algebra. In an illustration, our CPT-symmetric SUSY QM leads to non-Hermitian polynomial oscillators with real spectrum which turn out to be PT-asymmetric.
Nonlinear (Polynomial, N-fold) SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. Possible extensions of SUSY in one dimension are described. They include (no more than) ${\cal N} =2$ extended SUSY with two nilpotent SUSY charges which generate the hidden symmetry acting as a central charge. Embedding stationary quantum systems into a non-stationary SUSY QM is shown to yield new insight on quantum orbits and on spectrum generating algebras.
The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are investigated in detail. The particular case of diagonal initial Hamiltonian is considered, and the existence of solutions is demonstrated. Explicit examples illustrate the construction.
The connection between the thermodynamics of charged finite nuclear systems and the asymptotically measured partitions is presented. Some open questions, concerning in particular equilibrium partitions are discussed. We show a detailed comparison of the decay patterns in Au+ C,Cu,Au central collisions and in Au quasi-projectile events. Observation of abnormally large fluctuations in carefully selected samples of data is reported as an indication of a first order phase transition (negative heat capacity) in the nuclear equation of state.
We study SUSY-intertwining for non-Hermitian Hamiltonians with special emphasis to the two-dimensional generalized Morse potential, which does not allow for separation of variables. The complexified methods of SUSY-separation of variables and two-dimensional shape invariance are used to construct particular solutions - both for complex conjugated energy pairs and for non-paired complex energies.
Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in general. Some aspects of the spontaneous breakdown of PT symmetry are analysed.
Quasi-projectile events from peripheral 35 A.MeV Au+ Au collisions are compared to central Au + C, Au + Cu and Au + Au events in the same range of excitation energy in terms of critical partitions and critical exponents. All the different data sets coherently point to a value E*c=4.5 A.MeV for the apparent critical excitation energy. The critical exponents tau, sigma are compatible with the observation of a liquid-gas phase transition for these systems.
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations of Higher order SUSY Quantum Mechanics (HSUSY QM) with supercharges allowing for separation of variables. 2)The second one is a generalization of shape invariance. While in one dimension shape invariance allows to solve algebraically a class of (exactly solvable) quantum problems, its generalization to higher dimensions has not been yet explored. Here we provide a formal framework in HSUSY QM for two-dimensional quantum mechanical systems for which shape invariance holds. Given the knowledge of one eigenvalue and eigenfunction, shape invariance allows to construct a chain of new eigenfunctions and eigenvalues. These methods are applied to a two-dimensional quantum system, and partial explicit solvability is achieved in the sense that only part of the spectrum is found analytically and a limited set of eigenfunctions is constructed explicitly.
A global protocol for the thermostatistical analysis of hot nuclear sources is discussed. Within our method of minimization of variances we show that the abnormal kinetic energy fluctuation signal recently reported in different experimental data (M.D'Agostino et al.-Phys. Lett. B 473 (2000) 219, N. Le Neindre et al.- contr. to the XXXVIII Bormio Winter Meeting on Nucl. Phys. (2001) 404) is a genuine signal of a first order phase transition in a finite system.
The approach of multi-dimensional SUSY Quantum Mechanics is used in an explicit construction of exactly solvable 3-body (and quasi-exactly-solvable $N$-body) matrix problems on a line. From intertwining relations with time-dependent operators, we build exactly solvable non-stationary scalar and $2\times 2$ matrix 3-body models which are time-dependent extensions of the Calogero model. Finally, we investigate the invariant operators associated to these systems.
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY Quantum Mechanics providing a partnership between a real and a complex PT-symmetric potential of the kind mentioned above. We investigate conditions sufficient to ensure the reality of the full spectrum or, for the quasi-exactly solvable systems, the reality of the energy of the finite number of levels.