Regular Series

Vol. 29 (1998), No. 12, pp. 3543 – 3988

Where is the Higgs Boson?

Acta Phys. Pol. B 29, 3543 (1998)

page 3543 •


The status of the Higgs boson search in the Standard Model and beyond is presented.

Nonstandard Introduction to Squeezing of the Electromagnetic Field

Acta Phys. Pol. B 29, 3569 (1998)

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This article contains a review of an alternative theory of squeezing, based entirely on the wave function description of the squeezed states. Quantum field theoretic approach is used to describe the squeezing of the electromagnetic field in its most complete form that takes into account temporal and spatial characteristics of the squeezed state. An analog of the Wigner function for the full electromagnetic field is introduced and expressed in terms of second order correlation functions. The field-theoretic approach enables one to study the propagation of the “squeezing wave” in space-time. A simple example of weak squeezing, that allows for all calculations to be done analytically, is discussed in detail.

Effective Hamiltonians for Phonon and Spin Polarons

Acta Phys. Pol. B 29, 3591 (1998)

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Effective Hamiltonians for phonon and spin polarons are obtainedby applying a sequence of displacement and squeezing transformations to electron–phonon, or electron–magnon, interacting Hamiltonians. The basic techniques of calculation are shown in details, with explicit applications to the case of two- and four-sites systems.

Quantum Chaos: Entropy Signatures

Acta Phys. Pol. B 29, 3643 (1998)

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A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov–Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps.

Decoherence, Chaos, Quantum–Classical Correspondence and the Arrow of Time

Acta Phys. Pol. B 29, 3689 (1998)

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The environment — external or internal degrees of freedom coupled to the object of interest — can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states. Continuous destruction of superpositions leads to the effective environment-induced superselection (einselection), which is beginning to be recognized as a key step in the transition from quantum to classical. We investigate it here in the context of quantum chaos. I show that the evolution of a chaotic macroscopic system is not just difficult to predict (requiring accuracy exponentially increasing with time) but quickly ceases to be deterministic in principle as a result of the Heisenberg uncertainty (which limits the available resolution). This happens after a time \(t_{\hbar }\) which is only logarithmic in the Planck constant. For example, various components of the solar system are chaotic, with the Lyapunov timescales ranging from a bit more then a month (Hyperion) to millions of years (planetary system as a whole). On the timescale \(t_{\hbar }\) the initial minimum uncertainty wavepackets corresponding to celestial bodies would be smeared over distances of the order of radii of their orbits into “Schrödinger cat-like” states, and the very concept of a “trajectory” would cease to apply. In reality, such paradoxical states are eliminated by decoherence which helps restore quantum–classical correspondence. The price for the recovery of classicality is the loss of predictability. In the classical limit (associated not with the smallness of \(\hbar \), but with decoherence) the rate of increase of entropy is independent of the strength of the coupling to the environment, and equal to the sum of the positive Lyapunov exponents. I end by noting that the cost of information transfer between systems — of the action measured in units of \(\hbar \)’s per bit — decreases with the increasing size. This suggests why information may seem to be so irrelevant for classical dynamics, and yet is obviously so crucial at the quantum level.

Quark-Gluon Plasma

Acta Phys. Pol. B 29, 3711 (1998)

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An elementary introduction to the physics of quark–gluon plasma is given. We start with a sketchy presentation of the Quantum Chromodynamics which is the fundamental theory of strong interactions. The structure of hadrons built up of quarks and gluons is briefly discussed with a special emphasis on the confinement hypothesis. Then, we explain what is the quark–gluon plasma and consider why and when the hadrons can dissolve liberating the quarks and gluons. The heavy-ion collisions at high-energies, which provide a unique opportunity to get a droplet of the quark–gluon plasma in the terrestrial conditions, are described. We also consider the most promising experimental signatures of the quark–gluon plasma produced in nucleus–nucleus collisions. At the end, the perspectives of the quark–gluon plasma studies at the future accelerators are mentioned.

Bridging the Dimensional Gap: from Kink in One Dimension to Curved Domain Wall in Three Dimensions

Acta Phys. Pol. B 29, 3725 (1998)

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Improved expansion in width is applied to a curved domain wall in nonrelativistic dissipative \(\lambda ({\mit \Phi }^2 - v^2)^2 \) model with real scalar order parameter \({\mit \Phi }\). Approximate analytic description of such a domain wall to the second order in the width is presented.

Abelian–Higgs–Navier–Stokes Hydrodynamics for Nematic Films with Defects

Acta Phys. Pol. B 29, 3739 (1998)

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A new theory of hydrodynamics of uniaxial nematic liquid crystal films in the presence of defects is developed. A gauge field incorporating screening is introduced, resulting in the static elastic free energy having the form of a two-dimensional Abelian–Higgs model. Hydrodynamic equations are derived via the standard methods of de Groot and Mazur. By working in the vicinity of the Bogomol’nyi equations consequences for defect centre motion are outlined.

The Kondo Lattice Model

Acta Phys. Pol. B 29, 3753 (1998)

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In this lecture, we review the experimental situation of heavy fermions with emphasis on the existence of a quantum phase transition (QPT) and related non-Fermi liquid (NFL) effects. We overview the Kondo-Lattice Model (KLM) which is believed to describe the physics of those systems. After recalling the existing theories based on large-\(N\) expansion and various \(N\)=2 schemes, we present two alternative approaches: (i) a spin fluctuation Kondo functional integral approach treating the spin-fluctuation and Kondo effects on an equal footing, and (ii) a supersymmetric theory enlarging the usual fermionic representation of the spin into a mixed fermionic-bosonic representation in order to describe the spin degrees of freedom as well as the Fermi-liquid type excitations. This kind of approaches may open up new prospects for the description of the critical phenomena associated with the quantum phase transition in heavy-fermion systems.

Fermi and Non-Fermi Liquid Behavior in Quantum Impurity Systems: Conserving Slave Boson Theory

Acta Phys. Pol. B 29, 3781 (1998)

page 3781 •


The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong correlations is one of the prominent problems in metallic local moment systems. As standard models for such systems, the SU(\(N\))\(\times \)SU(\(M\)) Anderson impurity models exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their symmetry. Taking the Anderson model as an example, these lectures first give an introduction to the auxiliary boson method to describe correlated systems governed by a strong, short-range electronic repulsion. It is then shown how to include the relevant low-lying excitations (coherent spin flip and charge fluctuation processes), while preserving the local gauge symmetry of the model. This amounts to a conserving \(T\)-matrix approximation (CTMA). We prove a cancellation theorem showing that the CTMA incorporates all leading and subleading infrared singularities at any given order in a self-consistent loop expansion of the free energy. As a result, the CTMA recovers the correct infrared behavior of the auxiliary particle propagators, indicating that it correctly describes both the Fermi and the non-Fermi liquid regimes of the Anderson model.

Effective Gauge Theories the Renormalization Group and High-\(T_{\rm c}\) Superconductivity

Acta Phys. Pol. B 29, 3819 (1998)

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These lectures serve as an introduction to the renormalization group approach to effective field theories, with emphasis on systems with a Fermi surface. For such systems, demanding appropriate scaling with respect to the renormalization group for the appropriate excitations leads directly to the important concept of quasiparticles and the connexion between large-\(N_{\rm f}\) treatments and renormalization group running in theory space. In such treatments \(N_{\rm f}\) denotes the number of effective fermionic degrees of freedom above the Fermi surface; this number is roughly proportional to the size of the Fermi surface. As an application of these ideas, non-trivial infrared structure in three dimensional U(1) gauge theory is discussed, along with applications to the normal phase physics of high-\(T_{\rm c}\) superconductors, in an attempt to explain the experimentally observed deviations from Fermi liquid behaviour. Specifically, the direct current resistivity of the theory is computed at finite temperatures, \(T\), and is found to acquire \({\mathcal O}(1/N_{\rm f})\) corrections to the linear \(T\) behaviour. Such scaling corrections are consistent with recent experimental observations in high \(T{}_{\rm c}\) superconducting cuprates.

Luttinger-Liquid Phenomenology for High-\(T_{\rm c}\) Superconductors

Acta Phys. Pol. B 29, 3871 (1998)

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Universal scaling with temperature of the resistivity and optical conductivity in the normal state follows from the time-reversal symmetry assumed for the Green function with branch cuts combined with charge-spin separation. The density of states reproduces the extended van Hove singularity in a planar system. The single-particle tunneling conductivity in the superconducting state is nonzero at zero bias voltage, reproducing the pseudogap character of the density of states in the superconducting phase even for the \(s\)-wave symmetry of the order parameter. The form of the Ginzburg–Landau functional is also provided.

Particle-Hole Asymmetry in the BCS Thermodynamics

Acta Phys. Pol. B 29, 3885 (1998)

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It has been shown that the particle-hole asymmetry (PHA) of DOS leads to the first-order phase transition, a small deviation from the Luttinger theorem, and to very strange behaviour of subcritical specific heat. Because of the accuracy of the BCS thermodynamics in the thermodynamic limit (Bogolubov) it is strange that in trying to strengthen the theory while taking into account the tendency of DOS, we are in fact causing the deterioration of the theory. The answer lies in the retardation of the electron-phonon interaction for low temperature superconductors. Hence, if some elements of the BCS theory are applied for HTSC, it becomes necessary to be very careful in the question of thermodynamic properties. Moreover, the criteria of stability of the superconducting state has been formulated, at constant \(p\) and \(V\) as well, for one-component superconductors and isotropic Fermi superfluids. These criteria are free of the strong connection with the BCS model, they are purely thermodynamical. It is also shown that for the superconducting/superfluid Fermi systems the specific heat at constant \(p\) and \(V\) differ substantially, in contrast to any other low-temperature systems.

Phonon-Induced and Phonon-Free Superconductivity in Correlated Systems: Eliashberg Equations for the Two-Dimensional Hubbard Model

Acta Phys. Pol. B 29, 3907 (1998)

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The problem of phonon-induced and phonon-free superconductivity in the two-dimensional Hubbard model has been addressed. We have generalized the Eliashberg equations to account for both on-site and intersite pairing and consider the electron–electron and electron-phonon channels on an equal footing. This approach allows for the discussion of pairing and depairing properties of the local repulsive interaction. We demonstrate the possibility of cooperation between electron-phonon and electron–electron interaction in the stabilization of the d-wave superconductivity, in particular close to the experimental value of optimal doping (\(\delta \simeq 0.15\)). We have also discussed the problem of phonon-induced superconductivity in the two-dimensional Hubbard model close to the metal-insulator transition. Here, the Coulomb correlations have been incorporated within the Hubbard I approximation whereas the superconductivity is treated by the Eliashberg scheme. The results support the view that a d-wave component dominates in the gap function.

From Kaons to Neutrinos: Quantum Mechanics of Particle Oscillations

Acta Phys. Pol. B 29, 3925 (1998)

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The problem of particle oscillation is considered in a pedagogical and comprehensive way. Examples from \(K\), \(B\) and neutrino physics are given. Conceptual difficulties of the traditional approach to particle oscillation are discussed. It is shown how the probability current density and the wave packet treatments of particle oscillations resolve some problems. It is also shown that only full field theoretical approach is free from conceptual difficulties. The possibility of oscillation of particles produced together with kaons or neutrinos is considered in full wave packet quantum mechanics language. Precise definition of the oscillation of particles which recoil against mixed states is given. The general amplitude which describes the oscillation of two particles in the final states is found. Using this EPR-type amplitude the problem of oscillation of particles recoiling against kaons or neutrinos is resolved. The relativistic EPR correlations on distances of the order of coherence lengths are considered.

Chiral Random Matrix Models in QCD

Acta Phys. Pol. B 29, 3957 (1998)

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We review some motivation behind the introduction of chiral random matrix models in QCD, with particular emphasis on the importance of the Gell-Mann–Oakes–Renner (GOR) relation for these arguments. We show why the microscopic limit is universal in power counting, and present arguments for why the macroscopic limit is generic for a class of problems that defy power counting, examples being the strong CP and U(1) problems. We also discuss some of our new results in light of recent lattice simulations.


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