Exact crossover Green function in the two-channel and two-impurity Kondo models

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.     

An Order Model for Infinite Classical States

In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory, 2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and Martin is obtained. The infinite model retains many desirable aspects of the finite model, such as pure states as maximal elements and expected behavior of thermodynamic entropy. But it looses some of the important domain theoretic aspects, such as having a least element and exactness. Shannon entropy is no longer defined over the entire model and both it and thermodynamic entropy cease to be a measurements in the sense of Martin.     

The Investigation of Gauge Transformations in the SLq(2) Gauge Field and Thermodynamics Model

Some problems about global transformations in the SLq(2) gauge field and correlative thermodynamics model have been investigated in this paper. We proved that the quantum trace of gauge potential is not gauge-invariant if we compose two GLq(2) gauge transformations. In addition, it has been discovered in SLq(2) thermodynamics model that thermodynamics average of an observable quantity does not satisfy similar gauge invariance. We also found that the thermodynamics average can be only calculated in the case of zero energy gap. This fact shows that the q-deformed energy equation in superconductivity theory is unable to derive naturally from quantum trace model.     

Emergently thermalized islands in the landscape

In this Letter, we point out that in the eternal inflation driven by the metastable vacua of the landscape, it might be possible that some large and local quantum fluctuations with the null energy condition violation can stride over the barriers between different vacua and straightly create some islands with radiation and matter in new vacua. Then these thermalized islands will evolve with the standard cosmology. We show that such islands may be consistent with our observable universe, while has some distinctly observable signals, which may be tested in coming observations.     

Particle creation from vacuum by Lorentz violation

It is shown that the vacuum state in the presence of Lorentz violation can be followed by a universe filled with particles at late times similar to the current status of the universe. In this model a modification in dispersion relation (Lorentz violation) appears representing the regime of quantum gravity which has been dominant in the early universe. The existence of the particles can be interpreted as an evidence for quantum effects of gravity at early times. It is concluded that the present observable particles have a geometrical origin due to the well-known correspondence between geometry and gravity.     

Continuous QND measurements: no quantum noise

Monitoring an arbitrary observable is analyzed in the framework of Restricted-Path-Integral (RPI) theory of continuous quantum measurements. While in an usual (quantum-demolition) continuous measurement the measurement noise contains both classical and quantum parts, only the classical noise is shown to be present in a quantum nondemolition (QND) continuous measurement. As a result, no absolute restrictions exist on measurability of a QND observable and the measurement output satisfies the classical equation of motion. Monitoring the energy gives an example of a discrete-spectrum observable. Received: 7 April 1996 / Revised version: 7 August 1996     

Noncommutative coordinate picture of the quantum phase space

We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit coordinates and discuss the physical and dynamical picture. The isomorphism is then used as a base for the translation of the differential symplectic geometry of the infinite dimensional manifolds onto the observable algebra as a noncommutative geometry. Hence, we obtain the latter from the physical theory itself. We have essentially an extended formalism of the Schr̎odinger versus Heisenberg picture which we describe mathematically as like a coordinate map from the phase space, for which we have presented argument to be seen as the quantum model of the physical space, to the noncommutative geometry coordinated by the six position and momentum operators. The observable algebra is taken essentially as an algebra of formal functions on the latter operators. The work formulates the intuitive idea that the noncommutative geometry can be seen as an alternative, noncommutative coordinate, picture of familiar quantum phase space, at least so long as the symplectic geometry is concerned.     

Quantum Interference in Time

I discuss the interpretation of a recent experiment showing quantum interference in time. It is pointed out that the standard nonrelativistic quantum theory does not have the property of coherence in time, and hence cannot account for the results found. Therefore, this experiment has fundamental importance beyond the technical advances it represents. Some theoretical structures which consider the time as an observable, and thus could, in principle, have the required coherence in time, are discussed briefly, and the application of Floquet theory and the manifestly covariant quantum theory of Stueckelberg are treated in some detail. In particular, the latter is shown to account for the results in a simple and consistent way.     

Quantum state reconstruction via continuous measurement

We present a new procedure for quantum state reconstruction based on weak continuous measurement of an ensemble average. By applying controlled evolution to the initial state, new information is continually mapped onto the measured observable. A Bayesian filter is then used to update the state estimate in accordance with the measurement record. This generalizes the standard paradigm for quantum tomography based on strong, destructive measurements on separate ensembles. This approach to state estimation induces minimal perturbation of the measured system, giving information about observables whose evolution cannot be described classically in real time and opening the door to new types of quantum feedback control.     

Numerical Evidence of Quantum Correspondence to the Classical Ergodicity

Numerical experiment in Lipkin model shows that, in quantum system with global chaotic classical limit, the temporal mean of the expectation value of an observable is approximately equal to the average over the basic states of Hilbert space, if the wavefunction is initially either a coherent wave packet or the common eigenstates of a complete set of observables, and the observable is independent of the Hamiltonian. The mechanism is the absence of KAM barrier which prevents the spread of wavefunction. This can serve as a quantum signature of classical chaos.     

Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect

We investigate the weak decay of uniformly accelerated protons in the context of standard quantum field theory. Because the mean proper lifetime of a particle is a scalar, the same value for this observable must be obtained in the inertial and coaccelerated frames. We are only able to achieve this equality by considering the Fulling-Davies-Unruh effect. This reflects the fact that the Fulling-Davies-Unruh effect is mandatory for the consistency of quantum field theory.     

Correlation or decoherence? Quantum beats of atomic inversion in a resonant coherent field

It is shown that the standard reduction procedure (i.e., the calculation of the density matrix of the observable subsystem from the density matrix of a closed quantum system) bringing about decoherence corresponds to the limiting approximation, where the unobservable subsystem is assumed to be in the stationary state with minimum information (infinite temperature). An approximate set of interrelation (correlation) equations for the density matrices of the subsystems is derived. It is shown that the correlation of atom and field can be manifested as the inversion beats of a two-level atom in the known experimental scheme of resonator QED. Experimental observation of such beats would indicate that the observable subsystem (atom) generally conserves information about quantum coherence of the unobservable subsystem (field).     

Quantum Contextuality for a Three-Level System Sans Realist Model

Recently, an interesting form of non-classical effect which can be considered as a form of contextuality within quantum mechanics, has been demonstrated for a four-level system by discriminating the different routes that are taken for measuring a single observable. In this paper, we provide a simpler version of that proof for a single qutrit, which is also within the formalism of quantum mechanics and without recourse to any realist hidden variable model. The degeneracy of the eigenvalues and the Lüder projection rule play important role in our proof.     

Observable Correlations in Two-Qubit States

The total correlations in a bipartite quantum state are well quantified by the quantum mutual information, the amount of which is not necessarily fully extractable by local measurements. The observable correlations are the maximal correlations that can be extracted via local measurements, and have an intuitive interpretation as a measure of classical correlations. We evaluate the observable correlations for generic two-qubit states and obtain analytical expressions in some particular cases. The intricate and subtle relationships among the total, quantum and classical correlations are illustrated in terms of observable correlations. In the course, we also disprove an intuitive conjecture of Lindblad which states that the classical correlations account for at least half of the total correlations, or equivalently, correlations are more classical than quantum.     

Statistics of Local Value in Quantum Mechanics

Given a quantum mechanical observable and a state, one can construct a classical observable, that is, a real function on the configuration space, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. This optimal estimate turns out to be the quantum mechanical local value, which arises from several contexts such as de Broglie–Bohm's casual approach to quantum mechanics, instantaneous frequency in time–frequency analysis, Nelson's quantum fluctuations formalism, and phase-space approach to quantum mechanics. Accordingly, any observable can be decomposed into a local value part and a quantum fluctuation part, which are independent, both geometrically and statistically. Furthermore, the current density in quantum mechanics, the osmotic velocity in stochastic mechanics, and the Fisher information in classical statistical inference, arise naturally in connection with local value. In particular, Heisenberg uncertainty principle can be quantified more precisely by virtue of local value.     

An analog model for quantum lightcone fluctuations in nonlinear optics

We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable.     

Quantum mechanical measurement of non-orthogonal states and a test of non-locality

We propose a model of measurement of a non-hermitan observable whose states are described by non-orthogonal vectors. This model is used to analyse a proposal for testing non-locality in quantum mechanics using a system whose physically observable states are not mutually orthogonal.     

Minimal supersymmetric Higgs bosons with extra dimensions as the source of reheating and all matter

We consider the possibility that the dark energy responsible for inflation is deposited into extra dimensions outside of our observable Universe. Reheating and all matter can then be obtained from the minimal supersymmetric standard model flat direction condensate involving the Higgs bosons Hu and Hd, which acquires large amplitude by virtue of quantum fluctuations during inflation. The reheat temperature is TRH < or = 10(9) GeV so that there is no gravitino problem. We find a spectral index ns 1 with a very weak dependence on the Higgs potential.