Superposition Of Energy Eigenstates Research Articles

A self-consistent wave description of axion miniclusters and their survival in the galaxy

We present a solution of the Schrödinger-Poisson system based on the WKB ansatz for the wave function. In this way we obtain a description of a gravitationally bound clump of axion dark matter by a superposition of energy eigenstates with random phases. It can be applied to any self-consistent pair of radial density distribution and phase space density f(E) related by Eddington's formula. We adopt this as a model for axion miniclusters in our galaxy and use it to study the mass loss due to a star encounter by using standard perturbation theory methods known from quantum mechanics. Finally, we perform a Monte Carlo study to estimate the surviving fraction of axion miniclusters in the dark matter halo of our galaxy. We find that the reaction to perturbations and the survival probability depend crucially on the density profile. Weakly bound clusters are heated up and eventually destroyed, whereas more strongly bound systems get even more compact as a result of perturbations and are driven towards an axion star configuration.

Time-dependent dynamics of nuclear spin symmetry and parity violation in dichlorodisulfane (ClSSCl) during and after coherent radiative excitation

Parity and nuclear spin symmetry are approximate symmetries, which for many primary processes in molecular spectroscopy and kinetics lead to almost exact constants of the motion. The symmetric isotopomer dichlorodisulfane (disulfur dichloride) is chiral with two enantiomers, each of which has also two nuclear spin isomers (ortho and para isomers). Electroweak quantum chemistry predicts a small ‘parity violating’ energy difference between the ground states of the enantiomers (M being more stable than P by about ). Furthermore recent microwave spectroscopy has indicated ‘forbidden’ transitions between ortho and para isomers. These phenomena allow for a comparative study of the time-dependent quantum dynamics of parity and nuclear spin symmetry violation in a chiral molecule for the first time. We report quantum dynamical calculations of coherent radiative excitation of the complex manifold of polyads with hyperfine structure in ClSSCl. We demonstrate almost complete (near 100%) transfer of population from an almost pure para-ground state to an almost pure excited ortho state. Short-pulse excitation from the para-ground state to an excited time-dependent para chromophore state shows intramolecular interconversion between para and ortho nuclear spin isomers under isolation after the pulse on a time scale of a few nanoseconds to a few microsecond depending on the excited polyad. We also demonstrate the preparation of exotic ‘chameleon states’, which are superpositions of energy eigenstates corresponding to ortho- and para- nuclear spin symmetry isomers at the same time. The results are discussed in relation to the strong separation of time scales between the primary processes of nuclear spin symmetry isomerisation (nanoseconds to microseconds) and parity change (seconds) and in relation to possible experiments to measure in this molecule. We also compare with the rate processes of nuclear spin symmetry isomerisation induced by thermal black body radiation, depending on temperature, occurring on time scales from less than seconds to more than 100 years.

Measurement Induced Synthesis of Coherent Quantum Batteries

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

Catalytic coherence.

Because of conservation of energy we cannot directly turn a quantum system with a definite energy into a superposition of different energies. However, if we have access to an additional resource in terms of a system with a high degree of coherence, as for standard models of laser light, we can overcome this limitation. The question is to what extent coherence gets degraded when utilized. Here it is shown that coherence can be turned into a catalyst, meaning that we can use it repeatedly without ever diminishing its power to enable coherent operations. This finding stands in contrast to the degradation of other quantum resources and has direct consequences for quantum thermodynamics, as it shows that latent energy that may be locked into superpositions of energy eigenstates can be released catalytically.

Classical representation of wave functions for integrable systems

Classical exact $(\mathrm{CE})$ wave functions are certain integral representations of energy eigenfunctions that are parameterized in terms of the motion of the corresponding classical system in a semiclassically relevant way. When applied to systems for which they are not exact, such expressions serve as semiclassical approximations. Previous work identified $\mathrm{CE}$ wave functions for a number of specific systems and established their semiclassical usefulness. This paper explores the degree to which such representations can be found for more general systems. It is shown that $\mathrm{CE}$ wave functions exist, in principle, for bound states of an arbitrary integrable system that are confined to a single classically allowed region. Evidence is presented that $\mathrm{CE}$ representations also exist for more general states of such a system that are unbound, or that extend over more than one allowed region. The $\mathrm{CE}$ expressions are not unique: an innumerable variety exists for each such system. The existence proof provides a formal method for constructing $\mathrm{CE}$ expressions by Fourier transforming certain superpositions of energy eigenstates. The parameterization in terms of the classical motion is achieved by identifying certain quantities in these superpositions as classical action and angle variables. The semiclassical relevance of this identification is ensured by imposing some mild conditions on the coefficients in the superposition. This procedure for parameterizing exact wave functions in terms of classical variables indicates a basic relationship between the quantum and classical descriptions of states. The method of constructing $\mathrm{CE}$ wave functions introduced in the proof is shown to be consistent with a number of previously obtained $\mathrm{CE}$ formulas and is used to derive two new, closed-form, $\mathrm{CE}$ expressions. A simple numerical example is presented to illustrate the semiclassical application of one of these expressions and to further verify the physical significance of the classical parameterization.

“TIME ARROW” IN WAVE-PACKET EVOLUTION

Availability of short, femtosecond laser pulses has recently made feasible the probing of phases in an atomic or molecular wave-packet (superposition of energy eigenstates). With short duration excitations the initial form of the wave-packet is an essentially real “doorway state,” and this develops phases for each of its component amplitudes as it evolves. It is suggested that these phases are hallmarks of a time arrow and irreversibility that are inherent in the quantum mechanical processes of preparation and evolution. To display the non-triviality of the result, we show under what conditions it would not hold; to discuss its truth, we consider some apparent contradictions. We propose that (in time-reversal invariant systems) the preparation of “initially” complex wave-packets needs finite times to complete, i.e., is not instantaneous.

Local ergodicity as a probe for chaos in quantum systems: Application to the Henon–Heiles system

Classical chaos is usually accompanied by ‘‘local’’ ergodicity—ergodic behavior in regions of phase space that are generally smaller than, but of the same dimensionality as, the energy surface. If there are strong bottlenecks in phase space impeding the relaxation to statistical equilibrium in the full region of ergodicity, it is often possible to define an approximate form of ergodic behavior in a smaller subregion where relaxation occurs temporarily but quickly. Such ‘‘pseudoergodicity’’ is also a symptom of chaos. We use the presence of quantum behavior that mimics local ergodicity and pseudoergodicity as a probe for the influence of classical chaos on quantum dynamics. We show that the quantum analog of a pseudoergodic region in phase space is generally formed by superpositions of energy eigenstates. The superposition states spanning a given pseudoergodic zone have similar expectation values and small off-diagonal elements to other states with similar energy for a certain class of operators. We perform calculations which identify the ergodic regions for two versions of the quantum Henon–Heiles system. For the ‘‘more classical’’ of these systems we find good agreement between the proportion of quantum states in pseudoergodic zones and the proportion of classical phase space occupied by chaotic trajectories. We also find that the quantum pseudoergodic regions can be identified with classical vague tori of the precessing and librating types. Different ergodic regions are separated from one another by what appear to be the quantum analogs of the precessor–librator separatrix and other classical bottlenecks. For the ‘‘less classical’’ of the systems, we find that classical chaos is reflected in the quantum dynamics to a smaller, but still noticeable, degree.

Good and bad ghosts in quantum electrodynamics

A certain analogy of the indefinite metric in Gupta-Bleuler quantum electrodynamics and the Heisenberg Lee model is indicated. The state space of Gupta-Bleuler quantum electrodynamics and of the Lee model in the Heisenberg limiting case of coinciding V-particle solutions are both characterized by the appearance of unphysical states in the form of ghost couples consisting of two nonorthogonal states of zero norm. A physical interpretation of both theories is obtained by eliminating one of these ghosts, the «bad ghost», by a time-independent projection which in quantum electrodynamics is achieved by requiring the Lorentz condition in the Gupta form, in the Heisenberg Lee model by the condition that physical states must be superpositions of energy eigenstates. The other ghost state, the «good ghost», is not eliminated by this projection but does not contribute to matrix elements of observables due to its vanishing norm. In quantum electrodynamics the admixture of good ghosts to physical states is left arbitrary and reflects the arbitrariness of gauges within the Lorentz gauge; in the Lee model, however, its admixture is fixed as heisenberg has shown by securing a physical asymptotic behaviour of the scattering states. Virtually both the physical and unphysical states contribute to physical processes since only combined they represent a complete basis of the local operator algebra. The ghosts of quantum electrodynamics with interaction differ from the corresponding ghosts of the free theory. They are related by a nonlocal pseudounitary transformation. Introducing ghost-dressed field operators with the aid of this transformation leads to the Dirac-Schwinger formulation of quantum electrodynamics where the bad-ghost dressing of the source particles produces their Coulomb interaction. A similar elimination of the ghost structure in the Lee model appears to be possible but is not treated in the present paper.