Quantum instantons and quantum chaos

We suggest a closed form expression for the path integral of quantum transition amplitudes to construct a quantum action. Based on this we propose rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.     

Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions, including the exponential expansion solutions of the scalar factor a for the bubble. We show that exponential expansion of the bubble continues with a short period, no matter whether the bubble is closed, flat, or open. The exponential expansion ends spontaneously when the bubble becomes large, that is, the scalar factor a of the bubble approaches a Planck length lp. We show that it is the quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.     

Numerical study of metastability due to tunneling: The quantum string method

We generalize the string method, originally designed for the study of thermally activated rare events, to the calculation of quantum tunneling rates. This generalization is based on the formal analogy between quantum mechanics and statistical mechanics in the path-integral formalism. The quantum string method first locates the minimal action path (MAP), which is a smooth curve connecting two minima of the imaginary-time action in the space of imaginary-time trajectories. From the MAP, the saddle point of the action (called “the bounce”) associated with the exponential factor for barrier tunneling probability is obtained and the pre-exponential factor (the ratio of determinants) for the tunneling rate evaluated using stochastic simulation. The quantum string method is implemented to calculate the bounce and rate of tunneling for the Mueller potential in two dimensions. The quantum problem is much more difficult than the thermally activated barrier crossing problem for the same potential. The model calculations show the string method to be an efficient numerical tool for the study of barrier tunneling in higher dimension, from the determination of the saddle point to the computation of the pre-exponential factor.     

Universality of the continuum limit of lattice quantum theories

The lattice approximation of the naïve continuum action in quantum mechanics or in field theory is not uniquely determined. We investigate to what extent corrections to the lattice action, which vanish in the naïve continuum limit, affect the continuum limit when taking quantum fluctuations into account. In the quantum mechanical case, modifications of the lattice action may induce non-trivial corrections to the potential of the system and thereby change the structure of the theory completely. We verify this statement analytically as well as numerically by performing a Monte Carlo simulation. In the field theoretical case we argue that the lattice corrections considered do not affect the physics of the continuum limit, at least not for asymptotically free gauge field theories. In four dimensions, one might encounter finite renormalization of CP violating terms.     

Equivalence Postulate and Quantum Origin of Gravitation

We suggest that quantum mechanics and gravity are intimately related. In particular, we investigate the quantum Hamilton–Jacobi equation in the case of two free particles and show that the quantum potential, which is attractive, may generate the gravitational potential. The investigation, related to the formulation of quantum mechanics based on the equivalence postulate, is based on the analysis of the reduced action. A consequence of this approach is that the quantum potential is always non-trivial even in the case of the free particle. It plays the role of intrinsic energy and may in fact be at the origin of fundamental interactions. We pursue this idea, by making a preliminary investigation of whether there exists a set of solutions for which the quantum potential can be expressed with a gravitational potential leading term which alone would remain in the limit 0. A number of questions are raised for further investigation.     

Thermodynamics of quantum dissipative many-body systems

We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits us to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi(4) chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.     

The propagator of the Calogero-Moser system in an external quadratic potential

We obtain the Hamilton operator of the Calogero-Moser quantum system in an external quadratic potential by conjugating the radial part for the action of SO(n) by conjugacy of the Hamilton operator of the quantum harmonic oscillator on the Euclidean vector space of real symmetric matrices. Then, with Mehler's formula, we derive the propagator of the problem. We also investigate some schemes to change the interaction constant. For two-particle systems, we obtain explicit formulae, whereas for many-particle systems, we reduce the computation of the propagator to finding a definite integral. We give also the short time approximation, the energy levels and the trace of the propagation operator.     

Quantum effects on the competition between antiferromagnetism and superconductivity in heavy-fermion systems

We study a Ginzburg-Landau theory of two coupled fields describing superconductivity and antiferromagnetism in a metal. A coupling between the two-components superconductor and the antiferromagnetic (AF) field is included in the classical action. The classical results are improved calculating the quantum corrections to one-loop order with the method of the effective potential near the AF phase, but in the paramagnetic side. We discuss the influence of these corrections, including the possibility of fluctuation induced first order transitions. A scaling approach is used to obtain the critical and shift exponents at a quantum bicritical point.     

Ratchet effects in quantum wells with a lateral superlattice

Experimental and theoretical works on the ratchet effects in quantum wells with a lateral superlattice excited by alternating electric fields of terahertz frequency range has been reviewed. We discuss the Seebeck ratchet effect and helicity driven photocurrents and show that the photocurrent generation is based on the combined action of a spatially periodic in-plane potential and a spatially modulated light.     

Brownian motion of a classical particle in quantum environment

The Klein–Kramers equation, governing the Brownian motion of a classical particle in a quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.     

Quantum spin chains with quantum group symmetry

We consider actions of quantum groups on lattice spin systems. We show that if an action of a quantum group respects the local structure of a lattice system, it has to be an ordinary group. Even allowing weakly delocalized (quasi-local) tails of the action, we find that there are no actions of a properly quantum group commuting with lattice translations. The non-locality arises from the ordering of factors in the quantum groupC ^*-algebra, and can be made one-sided, thus allowing semi-local actions on a half chain. Under such actions, localized quantum group invariant elements remain localized. Hence the notion of interactions invariant under the quantum group and also under translations, recently studied by many authors, makes sense even though there is no global action of the quantum group. We consider a class of such quantum group invariant interactions with the property that there is a unique translation invariant ground state. Under weak locality assumptions, its GNS representation carries no unitary representation of the quantum group.Supported in part by NSF Grant # PHY90-19433 A02Copyright © 1995 by the authors. Faithful reproduction of this article by any means is permitted for non-commercial purposes.     

Action-variable perturbation theory

A quantum mechanical perturbation theory based upon the recently introduced quantum action variable is developed and illustrated. Unlike Rayleigh-Schrödinger or other asymptotic theories, this theory can provide a natural solution for the bound states of any potential.     

Non-local implementation of single-qubit rotation operation

We present two optimal schemes for non-local inplementing a single-qubit rotation operation via a maximally entangled quantum channel. We report on the quantitative relations between the quantum action,entangled and classical communication resources required in the implementation. We also put forward two schemes for conclusive implementing the non-local quantum single-qubit rotation via a partially entangled quantum channel. Both these methods can appropriately be referred to as qubit-assisted processes.     

Response of a system of strongly interacting particles to an inhomogeneous external field

We show that a system of N strongly interacting quantum particles in a parabolic confining potential can be unstable under the action of a time-dependent quadrupole external field. The instability leads to the generation or amplification of dipole oscillations. Parameters of the instability are independent of the number of particles and the inter-particle interaction.     

Spherical quantum dot in modified Kratzer–Coulomb potential: study of optical rectification coefficients

We consider the effects of quantum dot radius, confinement potential depth and controllable effective mass on the optical rectification coefficient (ORC) in spherical quantum dots, which is confined with Modified Kratzer–Coulomb Potential (MKCP). Using the Nikiforov–Uvarov method and compact density matrix theory, the ground state energy, ORC and wave function of electrons under the combined action of many factors are calculated. The results show that they affect the optical rectification response from different angles, including the position of peak and formant.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory(GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93(2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Stimulated emission from the biexciton in a single self-assembled II-VI quantum dot

Using two-photon excitation, stimulated emission from the biexciton state in a single CdSe/ZnSe quantum dot is observed in a two-pulse configuration. We directly time resolve the emission-absorption characteristics and verify the potential for laser action. By setting the polarization of the stimulation pulse, the recombination path of the biexciton and, by this, the state of the photons emitted in the decay cascade is controlled. We elaborate also the coherent response and address entanglement and disentanglement of the exciton-biexciton system.