Quantum field theory of optical birefringence phenomena

The inverse Faraday effect, in which a magnetization is induced in a solution through which is passed a polarized light beam of arbitrary ellipticity, is discussed on the basis of the S-matrix formulation of optical birefringence. It is shown that the Faraday effect and the inverse Faraday effect are topologically identical problems of diagrammatic perturbation theory and so it follows automatically that the magnetization should be proportional to the Verdet constant. The optical Faraday effect is the circular birefringence induced by an intense circularly polarized beam of light propagated colinearly with the weak measuring beam: the electric vector of the circularly polarized beam interacts with the molecule in a way that resembles the interaction of a static magnetic field. The interrelations of these two effects and the normal Faraday effect the self-rotation of the polarization ellipse of an intense beam are discussed.     

Quantum phenomena in gravitational field

The subjects presented here are very different. Their common feature is that they all involve quantum phenomena in a gravitational field: gravitational quantum states of ultracold antihydrogen above a material surface and measuring a gravitational interaction of antihydrogen in AEGIS, a quantum trampoline for ultracold atoms, and a hypothesis on naturally occurring gravitational quantum states, an Eötvös-type experiment with cold neutrons and others. Considering them together, however, we could learn that they have many common points both in physics and in methodology.     

Quantum tricriticality in transverse Ising-like systems

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3 ≤ d < 4, with a clear location of the critical lines ending in the conventional quantum critical points and in the quantum tricritical one, and of the tricritical line for temperature T ≥ 0. We determine also the critical and the tricritical shift exponents close to the corresponding ground state instabilities. Remarkably, we find a tricritical shift exponent identical to that found in the conventional quantum criticality and, by approaching the quantum tricritical point increasing the non-thermal control parameter r, a crossover of the quantum critical shift exponents from the conventional value φ = 1/(d − 1) to the new one φ = 1/2(d − 1). Besides, the projection in the (r,T)-plane of the phase boundary ending in the quantum tricritical point and crossovers in the quantum tricritical region appear quite similar to those found close to an usual quantum critical point. Another feature of experimental interest is that the amplitude of the Wilsonian classical critical region around this peculiar critical line is sensibly smaller than that expected in the quantum critical scenario. This suggests that the quantum tricriticality is essentially governed by mean-field critical exponents, renormalized by the shift exponent φ = 1/2(d − 1) in the quantum tricritical region.     

Some characteristic phenomena in a transverse Ising nanotube

The phase diagram and magnetizations of a cylindrical nanotube described by the transverse Ising model are investigated by the use of the effective field theory with correlations. Some comparisons between the nanotube and the nanowire have been given for the phase diagrams. In particular, the temperature dependences of longitudinal magnetization in the system with a negative shell–core interaction are investigated. Some characteristic phenomena (new types in ferrimagnetism) which have not been observed in the nanowire as well as similar phenomena are found in the thermal variations, depending on the ratio of the physical parameters in the surface shell and the core. The possibilities of two compensation points and a field induced compensation point in the nanotube are also discussed.     

Quantum holonomy theory

We present quantum holonomy theory, which is a non‐perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a ‐algebra that involves holonomy‐diffeo‐morphisms on a 3‐dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi‐classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi‐classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi‐classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost‐commutative algebra emerges from the holonomy‐diffeomorphism algebra in the same limit.     

Quantum circuit theory

The electronic Schroedinger Equation for devices which are small compared to the inelastic scattering length of electrons is solved by a transformation to an equivalent quantum circuit which is numerically tractable. The method is applied to dirty wires and reveals the existence of anomalously conductive states.     

Quantum phenomena in glasses at low temperatures

Glasses exhibit surprising low-temperature properties caused by the tunneling motion of small atomic clusters. We report here on recent dielectric measurements on a glass with the components BaO–Al₂O₃–SiO₂. In contrast to expectation, below 100 mK the dielectric properties become sensitive to weak magnetic fields. In this temperature range dielectric constant and dielectric loss show an oscillatory behavior with increasing magnetic field. Below 6 mK a phase transition within the ensemble of tunneling systems is observed.     

Quantum phenomena and the zeropoint radiation field

The stationary solutions for a bound electron immersed in the random zeropoint radiation field of stochastic electrodynamics are studied, under the assumption that the characteristic Fourier frequencies of these solutions are not random. Under this assumption, the response of the particle to the field is linear and does not mix frequencies, irrespectively of the form of the binding force; the fluctuations of the random field fix the scale of the response. The effective radiation field that supports the stationary states of motion is no longer the free vacuum field, but a modified form of it with new statistical properties. The theory is expressed naturally in terms of matrices (or operators), and it leads to the Heisenberg equations and the Hilbert space formalism of quantum mechanics in the radiationless approximation. The connection with the poissonian formulation of stochastic electrodynamics is also established. At the end we briefly discuss a few important aspects of quantum mechanics which the present theory helps to clarify.On leave of absence at Mathematics Department, University College London. Gower Street, London WC1, U.K.     

Quantum information theory

A conceptual analysis of the classical information theory of Shannon (1948) shows that this theory cannot be directly generalized to the usual quantum case. The reason is that in the usual quantum mechanics of closed systems there is no general concept of joint and conditional probability. Using, however, the generalized quantum mechanics of open systems (A. Kossakowski 1972) and the generalized concept of observable (“semiobservable”, E.B. Davies and J.T. Lewis 1970) it is possible to construct a quantum information theory being then a straightforward generalization of Shannon's theory.     

The possibility of re-entrant phenomena induced by a transverse field in ultra-thin transverse Ising films

The phase diagrams and temperature dependences of magnetizations in ultra-thin transverse Ising thin films are studied by the use of both the effective-field theory with correlations (EFT) and the mean-field theory (MFA). Novel features, such as the possibility of re-entrant phenomena, are obtained for the magnetic properties in such systems with a zero transverse field at the surfaces, when the EFT is applied to them, although such features could not be found from the use of the MFA. When the transverse field at the surfaces takes a finite value, however, the re-entrant phenomena could not be found from the both formulations of the EFT and the MFA. Similar phenomena are then obtained in the phase diagrams by using the MFA and the EFT.     

Large transverse momentum phenomena in a hadronic bremsstrahlung model

We present a bremsstrahlung model which at large transverse momenta p_T leads to an inverse power law for the pion distribution in pp → π^±0 + X. The model predicts particle yields that increase with energy at fixed p_T (breaking Feynman scaling in a definite way) and provides an understanding of the excess of π⁺'s over π^?'s, and of the increase with p_T of the associated multiplicity in the direction opposite to the observed pion; it also accounts for proton to π⁺ ratios of order 1, but in a parameter-dependent way. The recently observed increase of the mean charged multiplicity in pp → p + MM with the transverse momentum of the projectile is also accounted for.     

Quantum theory of irreversibility

A generalization of the Gibbs–von Neumann entropy is proposed based on the quantum BBGKY (Bogolyubov–Born–Green–Kirkwood–Yvon) hierarchy as the non-equilibrium entropy for an N$N$-body system. By using a generalization of the Liouville–von Neumann equation describing the evolution of a density superoperator, the entropy production for an isolated system is calculated, being non-zero in general. The existence of a non-zero entropy production allows us, following the procedure of non-equilibrium thermodynamics to introduce a master matrix for which a microscopic expression is obtained. After this, as a test of our theory the quantum Boltzmann equation is derived in terms of a transition superoperator related to this master matrix.