Semi-classical approximations based on Bohmian mechanics

Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.

We are now in the beginning of quantum supremacy to build Quantum Computers (Q.C.). So, a theoretical roadmap is required. It seems experimental works in Q.C. is ahead, in comparison with theory. In this study, Nano-Refraction (N.R.), as basic concept in developing Quantum Photonic Computers (Q.P.C.), is defined and discussed. N.R., is quite different from classical macroscopic refraction. It plays major role in photon deflection, when it travels in few atomic layers from the boundary between two transparent materials. Specifically, when we’re looking for a theoretically intuitive explanation of how advanced materials work in atomic scales in atto-second regime. To explain N.R., mathematically, Quantum Electrodynamics (QED) may help. But QED, only can describe how N.R. occurs in Hilbert space and does not explain why it happens in Real space? Why attosecond optical pulses are squeezed in kilometers long optical fibers coiled in first reported development of Q.C. in 2020. Also, “Duality” has no reply in this area. For answering why?, in this paper, we’ll use Quantum Photonic (Q.P.) theoretical analysis. Q.P., is based on Bohmian mechanics with intuition physics belief and “Causality”. Bohm theory in shadow of Quantum Mechanics (Q.M.) has been mostly ignored and even boycotted during last 70 years. Q.P. corpuscular viewpoint of light, estimated both physically and mathematically with enough precision, that flight route of photons at first few molecular surfaces in boundary region is not refracted suddenly. As can be observed macroscopically in Snell’s refraction equation. But instead, N.R. is happened gradually in attosecond regime (figure 2). Finally, it asymptotes to macroscopic refraction, in large space-time scales according to “correspondence” principle. Errors in our theoretical analysis using Montecarlo time domain simulation, compared with experiments, always are much less than or at most five percent.

Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy dissipation. To this end, we discuss two different time-dependent methods. One is to introduce an effective time-dependent Hamiltonian, which leads to a classical equation of motion as a relationship among expectation values of quantum operators. We apply this method to a heavy-ion fusion reaction and discuss the role of dissipation on the penetrability of the Coulomb barrier. The other method is to start with a Hamiltonian with environmental degrees of freedom and derive an equation which the system degree of freedom obeys. For this, we present a new efficient method to solve coupled-channels equations, which can be easily applied even when the dimension of the coupled-channels equations is huge.

Aim of this paper is trying to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics: More specifically, this work starts dealing with: (i) the hermitian (but not selfadjoint) Time operator in non-relativistic quantum mechanics and in quantum electrodynamics; with (ii) idem, the introduction of Time and Space operators; and with (iii) the problem of the four-position and fourmomentum operators, each one with its hermitian and anti-hermitian parts, for relativistic spin-zero particles. Afterwards, other physical applications of non-selfadjoint (and even non-hermitian) operators are briefly discussed. We briefly mention how non-hermitian operators can indeed be used in physics [as it was done, elsewhere, for describing Unstable States]; and some considerations are added on the cases of the nuclear optical potential, of quantum dissipation, and in particular of an approach to the measurement problem in QM in terms of a chronon. This paper is largely based on work developed, along the years, in collaboration with V.S.Olkhovsky, and, in smaller parts, with P.Smrz, with R.H.A.Farias, and with S.P.Maydanyuk.

The black hole information puzzle can be resolved if two conditions are met. The first is that the information about what falls inside a black hole remains encoded in degrees of freedom that persist after the black hole completely evaporates. These degrees of freedom should be capable of purifying the information. The second is if these purifying degrees of freedom do not significantly contribute to the system's energy, as the macroscopic mass of the initial black hole has been radiated away as Hawking radiation to infinity. The presence of microscopic degrees of freedom at the Planck scale provides a natural mechanism for achieving these two conditions without running into the problem of the large pair-creation probabilities of standard remnant scenarios. In the context of Hawking radiation, the first condition implies that correlations between the in and out Hawking partner particles need to be transferred to correlations between the microscopic degrees of freedom and the out partners in the radiation. This transfer occurs dynamically when the in partners reach the singularity inside the black hole, entering the UV regime of quantum gravity where the interaction with the microscopic degrees of freedom becomes strong. The second condition suggests that the conventional notion of the vacuum's uniqueness in quantum field theory should fail when considering the full quantum gravity degrees of freedom. In this paper, we demonstrate both key aspects of this mechanism using a solvable toy model of a quantum black hole inspired by loop quantum gravity.

Bound electron states in highly charged ions are strongly influenced by the effects of relativity and quantum electrodynamics (QED). These effects induce shifts of the binding energies as well as corrections to observables related to atomic processes. In this work a numerical procedure is described and implemented in which the QED effects are treated as corrections to relativistic bound-state wavefunctions. This approach, which is based on the recently developed covariant evolution-operator formalism, allows for a merging of QED with the standard methods of many-body perturbation theory. In particular, it enables an evaluation of the combined effect of QED and electron correlation in few-electron systems. Numerical results for this effect are presented for the ground state energy of heliumlike ions. A detailed analysis of the contribution from the electron self-energy is carried out in both the Feynman and Coulomb gauge. It is found that the Feynman gauge suffers from large numerical cancellations and aquires significant contributions from terms involving multiple interactions with the nuclear potential (the so-called many-potential terms), while the Coulomb gauge is well suited for an approximate treatment based on terms involving only freely propagating electrons (the zero-potential terms). With the help of QED-corrected wavefunctions it is also possible to compute corrections to observables in basic atomic processes. In this work some of the one-loop QED corrections (those derivable from perturbed wavefunctions and energies) to the differential cross section and distribution of polarization in radiative recombination of initially bare uranium nuclei are evaluated, as well as the corresponding corrections to the ratio of the electric dipole and magnetic quadrupole transition amplitudes in the 2p3/2 → 1s radiative decay of hydrogenlike uranium. The results from these calculations are all of the expected magnitude, namely on the order of the fine-structure contant.

Loss of incoherence and determination of coupling constants in quantum gravity

The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ``overlapping degrees of freedom". We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, \ie using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory.\ \ The numerical tools used in this work are publicly available within the \verb|GPUniverse| package, \url{https://github.com/OliverFHD/GPUniverse}~.

The aim of this paper is to show the importance and applicability of non-self-adjoint operators for description of observables both in relativistic and nonrelativistic quantum mechanics, as well as in quantum electrodynamics. The paper considers (i) a maximally Hermitian (but non-self-adjoint) time operator in nonrelativistic quantum mechanics and in quantum electrodynamics and (ii) the problem of defining the four-dimensional coordinate and momentum operators describing relativistic particles with zero spin (each of these operators contains both Hermitian and anti-Hermitian parts). Some other applications of non-selfadjoint and non-Hermitian operators in physics are analyzed as well. The paper ends with an analysis of a few cases of T-non-invariant interactions, including quantum dissipation and nuclear optical potentials.

The time variable is considered in the quantum gravity theory and calculated explicitly in the framework of the chaotic inflationary scenario where the scalar matter field has a contribution to the time variable in addition to the gravity field. The time formulated under the semiclassical approximation is a natural extension of that in the classical orbital motion. A perturbation method is introduced in terms of the scalar mass to obtain analytically solvable expressions for the time. The Wheeler-DeWitt equation is solved numerically to ensure that the semiclassical approximation is well justified. We examine the obtained time in detail and find that it is reasonable to consider it as time in the region where the semiclassical approximation is well justified.

Consistency between quantum mechanical and general relativistic views of the world is a longstanding problem, which becomes particularly prominent in black hole physics. We develop a coherent picture addressing this issue by studying the quantum mechanics of an evolving black hole. After interpreting the Bekenstein-Hawking entropy as the entropy representing the degrees of freedom that are coarse-grained to obtain a semiclassical description from the microscopic theory of quantum gravity, we discuss the properties these degrees of freedom exhibit when viewed from the semiclassical standpoint. We are led to the conclusion that they show features which we call extreme relativeness and spacetime-matter duality---a nontrivial reference frame dependence of their spacetime distribution and the dual roles they play as the "constituents" of spacetime and as thermal radiation. We describe black hole formation and evaporation processes in distant and infalling reference frames, showing that these two properties allow us to avoid the arguments for firewalls and to make the existence of the black hole interior consistent with unitary evolution in the sense of complementarity. Our analysis provides a concrete answer to how information can be preserved at the quantum level throughout the evolution of a black hole, and gives a basic picture of how general coordinate transformations may work at the level of full quantum gravity beyond the approximation of semiclassical theory.

An extended Vlasov equation, derived from the time-dependent Hartree–Fock–Bogoliubov equation of motion, is used to study the effects of pairing on the nuclear density-density linear response function in semiclassical approximation. Within the approximations adopted here, the fluctuations of the pairing field are purely imaginary and play a crucial role in eliminating a spurious mode that gives fluctuations of the number of particle and in reproducing the correct value of the energy-weighted sum rule. The semiclassical approach seems to have some difficulty in describing pairing vibrations. Further work on this problem is needed.

The accuracy of the semiclassical theory of forward glory scattering for a state-to-state chemical reaction is investigated using a J-shifted Eckart parameterization for the scattering matrix element. The parameters are chosen initially to model the angular scattering of the H+D2→HD(vf=3)+D reaction, following D. Sokolovski (Chem. Phys. Lett., 370, 805 (2003)). Then the parameters are systematically varied to generate different scattering patterns. The theory assumes that the scattering amplitude can be expanded in a Legendre partial wave series (PWS). The theoretical techniques applied to the PWS include: a nearside–farside decomposition, and a local angular momentum (LAM) analysis; both techniques include resummations of the PWS. The semiclassical techniques used include: a uniform semiclassical approximation (USA), a primitive semiclassical approximation, a classical semiclassical approximation, an integral transitional approximation, a semiclassical transitional approximation and a semiclassical LAM. The LAM for the classical collision of two hard spheres is also employed. It is demonstrated that the USA can accurately describe glory oscillations for scattering angles on and near the forward direction (as defined by the axial caustic associated with the glory); in favourable cases the USA is accurate for sideward scattering angles and even for angles close to the backward direction.

In this work, we study two examples of frustrated magnetic systems whose degrees of freedom are spins (or pseudo-spins) on two-dimensional lattices. The first part presents the results obtained for the quantum compass model on a square lattice. This model is a minimal model for the orbital degrees of freedom of transition metal compounds. We use exact diagonalizations, quantum Monte Carlo simulations as well as a perturbative approach in order to study the ground state degeneracy in the thermodynamic limit and the type of order in the ground state. The second part of this work is devoted to the study of the magnetic properties of SrCu2(BO3)2, which is one of the few quasi two-dimensional quantum magnets whose magnetization curve as a function of the magnetic field shows plateaus. The magnetic degrees of freedom are described by a spin 1/2 Heisenberg model on the Shastry-Sutherland lattice in the presence of an external magnetic field. In order to study the magnetic properties at zero-temperature, we use perturbative continuous unitary transformations to derive an effective Hamiltonian in which the triplets Sz = 1 are particles moving on a background of singlets. This Hamiltonian is characterized by a kinetic energy dominated by correlated hopping, which let a particle hop only if there is another particle nearby. In order to better understand the effect of the correlated hopping, we start by studying a minimal model. By using exact diagonalizations, quantum Monte Carlo and a semi-classical approximation we show that the correlated hopping can stabilize a phase characterized by a condensation of pairs of particles and strongly favor supersolid phases. Next, we determine the zero-temperature phase diagram of the effective model by using a classical approximation. A comparison to previous theoretical works and experimental measurements shows that the Shastry-Sutherland model cannot reproduce the series of magnetization plateaus measured experimentally. This suggest that the residual interactions, which were neglected, could be crucial for SrCu2(BO3)2.

Despite the success of general relativity in explaining classical gravitational phenomena, several problems at the interface between gravitation and high energy physics remain open to date. The purpose of this thesis is to explore classical and quantum gravity in order to improve our understanding of different aspects of gravity, such as dark matter, gravitational waves and ination. We focus on the class of higher derivative gravity theories as they naturally arise after the quantization of general relativity in the framework of effective field theory. The inclusion of higher order curvature invariants to the action always come in the form of new degrees of freedom. From this perspective, we introduce a new formalism to classify gravitational theories based on their degrees of freedom and, in light of this classification, we argue that dark matter is no different from modified gravity. Additional degrees of freedom appearing in the quantum gravitational action also affect the behaviour of gravitational waves. We show that gravitational waves are damped due to quantum degrees of freedom and we investigate the backreaction of these modes. The implications for gravitational wave events, such as the ones recently observed by the Advanced LIGO collaboration, are also discussed. The early universe can also be studied in this framework. We show how ination can be accommodated in this formalism via the generation of the Ricci scalar squared, which is triggered by quantum effects due to the non-minimal coupling of the Higgs boson to gravity, avoiding instability issues associated with Higgs ination. We argue that the non-minimal coupling of the Higgs to the curvature could also solve the vacuum instability issue by producing a large effective mass for the Higgs, which quickly drives the Higgs field back to the electroweak vacuum during ination.