Semiclassical Level Research Articles

Gravitational waves and perspectives for quantum gravity

Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector. The same situation holds in the quantum theory of metric. At the same time, including the fourth derivative terms means the presence of massive ghosts, which are gauge-independent massive states with negative kinetic energy. At both classical and quantum level such ghosts violate stability and hence the theory becomes inconsistent. Several approaches to solve this contradiction were invented and we are proposing one more, which looks simpler than those what were considered before. We explore the dynamics of the gravitational waves on the background of classical solutions and give certain arguments that massive ghosts produce instability only when they are present as physical particles. At least on the cosmological background one can observe that if the initial frequency of the metric perturbations is much smaller than the mass of the ghost, no instabilities are present.

Quantum energetic causal sets

We propose an approach to quantum theory based on the energetic causal sets, introduced in Cort\^{e}s and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links and conserved at each event. Energetic causal set models differ from other spacetime-free causal set approaches, e.g. Ref. [2] proposed causal sets based on quantum information processing systems, and Ref. [3] proposed causal sets constructed out of standard model particles. Fundamentally there are amplitudes for causal processes in energetic causal sets, but no space-time. An embedding of the causal processes in an emergent space-time arises only at the semiclassical level. Hence, fundamentally there are no commutation relations, no uncertainty principle and, indeed, no $\hbar$. All that remains of quantum theory is the relationship between the absolute value squared of complex amplitudes and probabilities. Consequently, we find that neither locality, nor non locality, are primary concepts, only causality exists at the fundamental level.

From quantum-mechanical to classical dynamics in the central-spin model

We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S. Uhrig, Phys. Rev. B 88, 155305 (2013) by the explicit consideration of the conservation of the total spin. On the classical level, we compare the results of the classical equations of motions in absence and presence of an external field to the full quantum result obtained by density-matrix renormalization (DMRG). We show that for large bath sizes and not too low magnetic field the classical dynamics, averaged over Gaussian distributed initial spin vectors, agrees quantitatively with the quantum-mechanical one. This observation paves the way for an efficient approach for certain parameter regimes.

Asymptotic symmetries of Yang-Mills theory

Asymptotic symmetries at future null infinity (I+) of Minkowski space for electrodynamics with massless charged fields, as well as non-Abelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through I+ suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at I+ and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of I+. The current Ward identities include Weinberg's soft photon theorem and its colored extension.

Pair creation of rotating black holes

An exact and regular solution, describing a couple of charged and spinning black holes, is generated in an external electromagnetic field, via Ernst technique, in Einstein-Maxwell gravity. A wormhole instantonic solution interpolating between the two black holes is constructed to discuss, at the semi-classical level, the quantum process of creation rate, in an external magnetic field, of this charged and spinning black hole pair.

Three-dimensional fractional-spin gravity

Abstract Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern-Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal nonabelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(ℓ, ℓ ± 1) or gl(ℓ|ℓ ± 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell.The project was funded in part by F.R.S.-FNRS “Ulysse” Incentive Grant for Mobility in Scientific Research.

Towards many-dimensional real-time quantum theory for heavy-particle dynamics. I. Semiclassics in the Lagrange picture of classical phase flow

We study a quantum theory in terms of action decomposed function (ADF), a class of quantum wave function, towards many-dimensional applications to quantum dynamics of heavy particles as in chemical reactions. The equation of motion for the complex-valued amplitude of ADF represents a coupling between the internal diffusive motion of a wave packet and dynamics of its group velocity in a hierarchical manner ascending from classical to purely quantum mechanics via semiclassical dynamics. We attempt to solve this equation of motion dividing it into two stages: a semiclassical level and beyond. In this paper, as the first stage, we develop a semiclassical approximation in the Lagrange picture of classical phase flow. In the Euler picture (as in the standard WKB picture), continuous integration of the stability matrix along the paths is required. By adopting the Lagrange picture, on the other hand, we represent the semiclassical amplitude in terms of what we call deviation determinant, which can be evaluated readily in many-dimensional systems. Numerical tests show that ADF reproduces quantum wave packets at each space-time point along classical paths very well. However, the ADF in this stage is not free of the semiclassical singularity. In other words, the wave functions diverge at turning points or caustics, depending on the initial conditions chosen. This divergence is known to take place at points where classical paths smoothly distributed in phase space have ``focuses'' in configuration space (or momentum space) and reflects an intrinsic relationship between quantum and classical mechanics. Therefore, it is by studying the mechanism of removing the singularity that the essential feature of quantum mechanics will be clarified. This aspect will be discussed in a companion paper [K. Takatsuka and S. Takahashi, Phys. Rev. A 89, 012109 (2014)] as the second stage of many-body quantum theory.

Semiclassical propagation up to the Heisenberg time

By using a quantum Hamiltonian system with classically chaotic dynamics, we demonstrate that it is possible to propagate waves, at a semiclassical level, for extremely long times of the order of the Heisenberg time. We achieve this unexpected result with a new formula that evaluates the autocorrelation function of a quantum state living in the neighborhood of a short periodic orbit, the so-called resonance, in terms of the set of homoclinic orbits; this set is given by the intersection of the stable and unstable manifolds of the periodic orbit. Here we study the manifolds of the shortest periodic orbit of the hyperbola billiard (a chaotic Hamiltonian system), finding a surprisingly simple tree structure. Then, we compute a complete set consisting of the first 18 146 homoclinic orbits, and by using this data we analyze the convergence of the new formula. Finally, we compare the quantum and semiclassical autocorrelation of resonances up to the Heisenberg time, obtaining a relative error O(ℏ) in correspondence with semiclassical predictions.

The fate of monsters in anti-de Sitter spacetime

Abstract Black hole entropy remains a deep puzzle: where does such enormous amount of entropy come from? Curiously, there exist gravitational configurations that possess even larger entropy than a black hole of the same mass, in fact, arbitrarily high entropy. These are the so-called monsters, which are problematic to the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence paradigm since there is far insufficient degrees of freedom on the field theory side to account for the enormous entropy of monsters in AdS bulk. The physics of the bulk however may be considerably modified at semi-classical level due to the presence of branes. We show that this is especially so since monster spacetimes are unstable due to brane nucleation. As a consequence, it is not clear what the final fate of monsters is. We argue that in some cases there is no real threat from monsters since although they are solutions to Einstein’s Field Equations, they are very likely to be completely unstable when embedded in string theory, and thus probably are not solutions to the full quantum theory of gravity. Our analysis, while suggestive and supportive of the claim that such pathological objects are not allowed in the final theory, by itself does not rule out all monsters. We comment on various kin of monsters such as the “bag-of-gold” spacetime, and also discuss briefly the implications of our work to some puzzles related to black hole entropy.

On semiclassical equivalence of Green–Schwarz and pure spinor strings in AdS(5) × S(5)

We present a method to study the equivalence at the semiclassical level of the Green–Schwarz and pure spinor formulations of string theory in AdS(5) × S(5). This method provides a clear separation of the physical and unphysical sectors of the pure spinor formulation and allows us to prove that the two models have not only equal spectra of the fermionic fluctuations but also equal conformal weights (the bosonic ones being equal by construction).

Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula

We search for a universal property of quantum gravity. By "universal", we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this assumption, the conditions justifying Boltzmann formula together with uniqueness of Bekenstein-Hawking entropy imply a reasonable universal property of quantum gravity. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity. Further, in semi-classical level, we discuss a possible correction of Einstein equation which generates repulsive gravity at Planck length scale.

Periodic-orbit approach to nuclear shell structures with power-law potential models: Bridge orbits and prolate-oblate asymmetry

Deformed shell structures in nuclear mean-field potentials are systematically investigated as functions of deformation and surface diffuseness. As the mean-field model to investigate nuclear shell structures in a wide range of mass numbers, we propose the radial power-law potential model, V \propto r^\alpha, which enables a simple semiclassical analysis by the use of its scaling property. We find that remarkable shell structures emerge at certain combinations of deformation and diffuseness parameters, and they are closely related to the periodic-orbit bifurcations. In particular, significant roles of the "bridge orbit bifurcations" for normal and superdeformed shell structures are pointed out. It is shown that the prolate-oblate asymmetry in deformed shell structures is clearly understood from the contribution of the bridge orbit to the semiclassical level density. The roles of bridge orbit bifurcations in the emergence of superdeformed shell structures are also discussed.

De Sitter Tunneling, Emission Spectrum and Entropy/Area Quantum

The Banerjee—Majhi's recent work shows that the Hawking radiation and entropy/area quantum of the black hole horizon (EH) can be well described in the tunneling picture. In this paper, we develop this idea to the case of a de Sitter tunneling from the cosmological horizon (CH), and obtain the Hawking emission spectrum and entropy/area spectroscopy from the CH of the purely de Sitter black hole as well as the Schwarzschild-de Sitter black hole. It is interestingly found that the area of the CH is quantized by ΔA = 4l2pl, as was given by Hod for the area quantum of -the EH by considering the Heisenberg uncertainty principle and Schwinger-type emission process. Also, we conclude from our derivation that the entropy/area quantum of the CH is universal in the sense that it is independent of the black hole parameters. This realization implies that, (at least) at a semiclassical level, the de Sitter gravity shares the similar quantum behavior as the usual gravity without presence of a cosmological constant.

Quantum criticality in a bosonic Josephson junction

In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the discrete self-trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from quantum information theory, i.e., the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero-temperature case, but considers thermal effects as well.

Confining vacua in SQCD, the Konishi anomaly and the Dijkgraaf-Vafa superpotential

In this paper we revisit the analysis of vacua in N=2 SQCD with generic bare quark masses, softly broken by a mass term for the chiral superfield \Phi in the adjoint representation of the gauge group. These vacua are labelled by an integer r (r vacua) and can be studied at the semiclassical level by means of the equations of motion (for large mass) or nonperturbatively by means of the Seiberg-Witten curve (for small mass). Making use of the Konishi anomaly and of the Dijkgraaf-Vafa superpotential we are able to interpolate between these two limits and better understand the properties of these vacua. In particular, we clarify the origin of the two to one map that relates semiclassical to quantum vacua.

Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition

We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) equations at the quantum and semiclassical level, respectively. After showing that the gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite populations effects introducing a suitable scaling hypothesis; we work out the exact value of the critical exponents and we provide numerical evidences confirming our hypothesis. Our analytical results rely on a general scheme obtained from a large-population expansion of the eigenvalue equation of the BH model. In this approach the DST equations resurface as solutions of the zeroth-order problem.

Gauge theories as matrix models

We discuss the relation between the Seiberg-Witten prepotentials, Nekrasov functions, and matrix models. On the semiclassical level, we show that the matrix models of Eguchi-Yang type are described by instantonic contributions to the deformed partition functions of supersymmetric gauge theories. We study the constructed explicit exact solution of the four-dimensional conformal theory in detail and also discuss some aspects of its relation to the recently proposed logarithmic beta-ensembles. We also consider “quantizing” this picture in terms of two-dimensional conformal theory with extended symmetry and stress its difference from the well-known picture of the perturbative expansion in matrix models. Instead, the representation of Nekrasov functions using conformal blocks or Whittaker vectors provides a nontrivial relation to Teichmüller spaces and quantum integrable systems.

Phenomenology of gravitational aether as a solution to the old cosmological constant problem

One of the deepest and most long-standing mysteries in physics has been the huge discrepancy between the observed vacuum density and our expectations from theories of high energy physics, which has been dubbed the Old Cosmological Constant problem. One proposal to address this puzzle at the semi-classical level is to decouple quantum vacuum from space-time geometry via a modification of gravity that includes an incompressible fluid, known as Gravitational Aether. In this paper, we discuss classical predictions of this theory along with its compatibility with cosmological and experimental tests of gravity. We argue that deviations from General Relativity (GR) in this theory are sourced by pressure or vorticity. In particular, the theory predicts that the gravitational constant for radiation is 33% larger than that of non-relativistic matter, which is preferred by (most) cosmic microwave background (CMB), Lyman-Alpha forest, and Lithium-7 primordial abundance observations, while being consistent with other cosmological tests at ~2-sigma level. It is further shown that all Parametrized Post-Newtonian (PPN) parameters have the standard GR values aside from the anomalous coupling to pressure, which has not been directly measured. A more subtle prediction of this model (assuming irrotational aether) is that the (intrinsic) gravitomagnetic effect is 33% larger than GR prediction. This is consistent with current limits from LAGEOS and Gravity Probe B at ~2-sigma level.

Universal Property of Quantum Gravity implied by Uniqueness Theorem of Bekenstein-Hawking Entropy

This paper consists of three parts. In the first part, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion. In the second part, intrinsic properties of quantum mechanics are shown, which justify the Boltzmann formula to yield a unique entropy in statistical mechanics. These properties clarify three conditions, one of which is necessary and others are sufficient for the validity of Boltzmann formula. In the third part, by combining the above results, we find a reasonable suggestion from the sufficient conditions that the potential of gravitational interaction among microstates of underlying quantum gravity may not diverge to negative infinity (such as Newtonian gravity) but is bounded below at a finite length scale. In addition to that, from the necessary condition, the interaction has to be repulsive within the finite length scale. The length scale should be Planck size. Thus, quantum gravity may become repulsive at Planck length. Also, a relation of these suggestions with action integral of gravity at semi-classical level is given. These suggestions about quantum gravity are universal in the sense that they are independent of any existing model of quantum gravity.

The Bianchi I model in terms of nonstandard loop quantum cosmology: quantum dynamics

We analyze the quantum Bianchi I model in the setting of nonstandard loop quantum cosmology. Elementary observables are used to quantize the volume operator, and the spectrum of the volume operator is bounded from below and discrete. The discreteness may imply a foamy structure of spacetime at the semiclassical level. The results are described in terms of a free parameter specifying loop geometry to be determined in astro-cosmo observations. An evolution of the quantum model is generated by the so-called true Hamiltonian, which enables the introduction of a time parameter valued in the set of all real numbers.