Complex Calogero model with real energies

Complex Energies and Beginnings of Time Suggest a Theory of Scattering and Decay

Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the conventional (Hilbert space) axioms of quantum mechanics. Using the Lippmann-Schwinger equations as the takeoff point and aiming for a theory that unites resonances and decay, we conjecture a new axiom for quantum mechanics that distinguishes mathematically between prepared states and detected observables. Suggested by the two signs $\pm iε$ of the Lippmann…

Complex angular momentum theory of state-to state integral cross sections: resonance effects in the F+HD->HF(v'=3)+D reaction

State-to-state reactive integral cross sections (ICS) are often affected by quantum mechanical resonances, especially at relatively low energies. An ICS is usually obtained by summing partial waves at a given value of energy. For this reason, the knowledge of pole positions and residues in the complex energy plane is not sufficient for a quantitative description of the patterns produced by a resonance. Such description is available in terms of the poles of an S-matrix element in the complex plane of the total angular momentum. The approach was recently implemented in a computer code ICS_Regge,…

Second order SUSY transformations with `complex energies'

Second order supersymmetry transformations which involve a pair of complex conjugate factorization energies and lead to real non-singular potentials are analyzed. The generation of complex potentials with real spectra is also studied. The theory is applied to the free particle, one-soliton well and one-dimensional harmonic oscillator.

Chern-Simons theory, exactly solvable models and free fermions at finite temperature

We show that matrix models in Chern-Simons theory admit an interpretation as 1D exactly solvable models, paralleling the relationship between the Gaussian matrix model and the Calogero model. We compute the corresponding Hamiltonians, ground-state wavefunctions and ground-state energies and point out that the models can be interpreted as quasi-1D Coulomb plasmas. We also study the relationship between Chern-Simons theory on $S^3$ and a system of N one-dimensional fermions at finite temperature with harmonic confinement. In particular we show that the Chern-Simons partition function can be desc…

A Gauss Elimination Method for Resonances

A Gaussian elimination form of inverse iteration within the complex coordinate approach is shown to produce a simple uniform method of finding both real bound state energies and complex resonant state energies for several problems which have been treated by a variety of methods in the literature. The energy shift method for expectation values is shown to be a useful diagnostic tool.

Tunneling of Bound Systems at Finite Energies: Complex Paths Through Potential Barriers

We adapt the semiclassical technique, as used in the context of instanton transitions in quantum field theory, to the description of tunneling transmissions at finite energies through potential barriers by complex quantum mechanical systems. Even for systems initially in their ground state, not generally describable in semiclassical terms, the transmission probability has a semiclassical (exponential) form. The calculation of the tunneling exponent uses analytic continuation of degrees of freedom into a complex phase space as well as analytic continuation of the classical equations of motion i…

Density Functional Resonance Theory: complex density functions, convergence, orbital energies, and functionals

Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett. \textbf{107}, 163002 (2011)], a recently developed complex-scaled version of ground-state Density Functional Theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, $θ$. In Kohn-Sham…

Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a wave guide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential an…

Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors

We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and AC conductivity of a homogeneous superconductor with arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers--Kronig transforms. A number of applications illustrates its efficiency: a simplified low-frequency expansion of the conductivity,…

Complex BPS solitons with real energies from duality

Following a generic approach that leads to Bogomolny-Prasad-Sommerfield (BPS) soliton solutions by imposing self-duality, we investigate three different types of non-Hermitian field theories. We consider a complex version of a logarithmic potential that possess BPS super-exponential kink and antikink solutions and two different types of complex generalisations of systems of coupled sine-Gordon models with kink and antikink solution of complex versions of arctan type. Despite the fact that all soliton solutions obtainedin this manner are complex in the non-Hermitian theories we show that they p…

Complex-scaled ab initio QED approach to autoionizing states

Ab initio method based on a complex-scaling approach and aimed at a rigorous QED description of autoionizing states is worked out. The autoionizing-state binding energies are treated nonperturbatively in $αZ$ and include all the many-electron QED contributions up to the second order. The higher-order electron correlation, nuclear recoil, and nuclear polarization effects are taken into account as well. The developed formalism is demonstrated on the $LL$ resonances in heliumlike argon and uranium. The most accurate theoretical predictions for the binding energies are obtained.

Linearly stable and unstable complex soliton solutions with real energies in the Bullough-Dodd model

We investigate different types of complex soliton solutions with regard to their stability against linear pertubations. In the Bullough-Dodd scalar field theory we find linearly stable complex ${\cal{PT}}$-symmetric solutions and linearly unstable solutions for which the ${\cal{PT}}$-symmetry is broken. Both types of solutions have real energies. The auxiliary Sturm-Liouville eigenvalue equation in the stability analysis for the ${\cal{PT}}$-symmetric solutions can be solved exactly by supersymmetrically mapping it to an isospectral partner system involving a shifted and scaled inverse $\cosh$…

Suppression of quantum oscillations and the dependence on site energies in electronic excitation transfer in the Fenna-Matthews-Olson trimer

Energy transfer in the photosynthetic complex of the Green Sulfur Bacteria known as the Fenna-Matthews-Olson (FMO) complex is studied theoretically taking all three subunits (monomers) of the FMO trimer and the recently found eighth bacteriochlorophyll (BChl) molecule into account. We find that in all considered cases there is very little transfer between the monomers. Since it is believed that the eighth BChl is located near the main light harvesting antenna we look at the differences in transfer between the situation when BChl 8 is initially excited and the usually considered case when BChl …

Riccati、Ermakov 与 Schrödinger 方程之间的相互作用以产生具有实能谱的复值势

Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum

本文利用 Riccati 与 Ermakov 方程结合 Darboux 方法，构造能谱继承 Hermitian 可解系统全部能量且额外含一个实本征值且无奇点的复值势，并以 Morse 和三角 Pöschl-Teller 势为例说明。

Pseudo-Jahn-Teller interaction among electronic resonant states of H3

We study the electronic resonant states of H3 with energies above the potential energy surface of the H3+ ground state. These resonant states are important for the dissociative recombination of H3+ at higher collision energies, and previous studies have indicated that these resonant states exhibit a triple intersection. We introduce a complex generalization of the pseudo-Jahn-Teller model to describe these resonant states. The potential energies and the autoionization widths of the resonant states are computed with electron scattering calculations using the complex Kohn variational method, and…