The length operator in Loop Quantum Gravity

The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity—the length operator. We describe its quantum geometrical meaning and derive some of its properties. In particular we show that the operator has a discrete spectrum and is diagonalized by appropriate superpositions of spin network states. A series of eigenstates and eigenvalues is presented and an explicit check of its semiclassical properties is discussed.     

Spin geometry of entangled qubits under bilocal decoherence modes

The Lindblad generators of the master equation define which kind of decoherence happens in an open quantum system. We are working with a two qubit system and choose the generators to be projection operators on the eigenstates of the system and unitary bilocal rotations of them. The resulting decoherence modes are studied in detail. Besides the general solutions we investigate the special case of maximally entangled states—the Bell singlet states. The results are depicted in the so-called spin geometry picture which allows to illustrate the evolution of the (nonlocal) correlations stored in a certain state. The question for which conditions the path traced out in the geometric picture depends only on the relative angle between the bilocal rotations is addressed.     

The emergence of background geometry from quantum fluctuations

We show how the quantization of two-dimensional gravity leads to an (Euclidean) quantum space–time where the average geometry is that of constant negative curvature and where the Hartle–Hawking boundary condition arises naturally.     

Alternative quantization of the Hamiltonian in loop quantum cosmology

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities. In this Letter, we quantize the Lorentz term of the gravitational Hamiltonian constraint in the spatially flat FRW model by two approaches different from that of the Euclidean term. One of the approaches is very similar to the treatment of the Lorentz part of Hamiltonian in loop quantum gravity and hence inherits more features from the full theory. Two symmetric Hamiltonian constraint operators are constructed respectively in the improved scheme. Both of them are shown to have the correct classical limit by the semiclassical analysis. In the loop quantum cosmological model with a massless scalar field, the effective Hamiltonians and Friedmann equations are derived. It turns out that the classical big bang is again replaced by a quantum bounce in both cases. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect.     

Asymptotics of 4d spin foam models

We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary data. For some classes of geometrical boundary data, the asymptotic formulae are given, in all three cases, by simple functions of the Regge action for the four-simplex geometry.     

Hadron Physics from Superconformal Quantum Mechanics and Its Light-Front Holographic Embedding

The complex nonperturbative color-confining dynamics of QCD is well captured in a semiclassical effective theory based on superconformal quantum mechanics and its extension to the light-front. I describe here how this new approach to hadron physics incorporates confinement, the appearance of nearly massless pseudoscalar particles, and Regge spectroscopy consistent with experiment. It also gives remarkable connections between the meson and baryon spectrum across the light and heavy-light hadron spectrum. I also briefly discuss how higher spin states are consistently described in this framework by the holographic embedding of the superconformal theory in a higher dimensional semiclassical gravity theory.     

Giant paramagnetism in Li-doped Mo-S nanostructures

Magnetic measurements of Li-doped MoS_2−y nanostructures show a peculiarly large T-independent paramagnetic signal, which cannot be understood in terms of either Curie- or Pauli paramagnetism, or—for that matter—in terms of any simple spin-correlated state, such as antiferromagnetism or superparamagnetic spin clustering. This behaviour appears to be a result of a near-ideal one-dimensional (1D) strongly correlated state, due to the extraordinarily weak inherent coupling between 1D subunits (nanotubes or nanowires), which is an order of magnitude weaker even than in carbon nanotube ropes. In spite of clear evidence for strong electronic correlations from a giant paramagnetic susceptibility, no transition to an ordered state is observed down to very low temperatures and the system appears to be stabilised in a paramagnetic state by fluctuations characteristic of 1D systems. Down to 2 K there is no evidence of a low-temperature quantum critical point.     

The Casimir effect for fields with arbitrary spin

The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.     

Quantum fluctuations in Sine-Gordon like magnetic chains: Corrections to soliton energies

The effect of quantum fluctuations on solitons in the easy-plane ferromagnetic chain is considered within the semiclassical approximation. In accordance with the low temperature ideal gas picture we treat the solitons as a Boltzmann gas and impose quantisation on the spin wave spectrum. We present a method which allows to calculate quantum corrections in a systematic perturbation expansion in 1/S, whereS is the spin length. We use this method to obtain the soliton energy to second order at zero temperature. Our results indicate that the semiclassical approach reasonably describes quantum effects on soliton properties.     

Competing boundary interactions in a Josephson junction network with an impurity

We analyze a perturbation of the boundary Sine-Gordon model where two boundary terms of different periodicities and scaling dimensions are coupled to a Kondo-like spin degree of freedom. We show that, by pertinently engineering the coupling with the spin degree of freedom, a competition between the two boundary interactions may be induced, and that this gives rise to nonperturbative phenomena, such as the emergence of novel quantum phases: indeed, we demonstrate that the strongly coupled fixed point may become unstable as a result of the “deconfinement” of a new set of phase-slip operators — the short instantons — associated with the less relevant boundary operator. We point out that a Josephson junction network with a pertinent impurity located at its center provides a physical realization of this boundary double Sine-Gordon model. For this Josephson junction network, we prove that the competition between the two boundary interactions stabilizes a robust finite coupling fixed point and, at a pertinent scale, allows for the onset of 4e superconductivity.     

Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at “quantum scales” and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a “semiclassical” state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity.     

Discrete quantum gravity in the Regge calculus formalism

We discuss an approach to the discrete quantum gravity in the Regge calculus formalism that was developed in a number of our papers. The Regge calculus is general relativity for a subclass of general Riemannian manifolds called piecewise flat manifolds. The Regge calculus deals with a discrete set of variables, triangulation lengths, and contains continuous general relativity as a special limiting case where the lengths tend to zero. In our approach, the quantum length expectations are nonzero and of the order of the Plank scale, 10^?33 cm, implying a discrete spacetime structure on these scales.     

Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order ħ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.     

Quantum to classical correspondence for the Fermi-acceleration model

A quantum particle which is confined to the interior of a box with infinitely high but periodically oscillating walls can have an unusual semiclassical limit: For the special case of a one-dimensional linear wall motion we show that the semiclassical domain corresponds to a classical motion in phase space where the initial momentum depends on the particle's position in the box. Another result is that quantum states which correspond to classical cycle-1 fixed points have maximum stability against the boundary induced perturbation (caused by the moving wall). Higher cycle-n fixed points are calculated by numerical bookkeeping up to n = 20. The classical motion is marginally stable. We show how a slight change in the boundary condition will lead to chaotic motion.     

Classical and Quantum Theories of Spin

A great effort has been devoted to formulating a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in connecting classical and quantum theories rests in finding a parameter that plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneering works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level, we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail.     

Feynman propagator for spin foam quantum gravity

We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".     

Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space–time dimension

A profound quantum-gravitational effect of space–time dimension running with respect to the size of space–time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this Letter is twofold. First, we find that box-counting dimension in face of finite resolution of space–time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood. Second, considering two most interesting cases of random and holographic fluctuations of the background space, we find that it is random fluctuations that gives running dimension resulting in modification of Newton's inverse square law in a perfect agreement with the modification coming from one-loop gravitational radiative corrections.