Semiclassical Quantization Research Articles

Semiclassical Analysis, Geometric Representation and Quantum Ergodicity

Semiclassical Analysis, Geometric Representation and Quantum Ergodicity

‘IT FROM BIT’: How does information shape the structures in the Universe?

Based on a synthesis of three main ingredients: (i) the Shannon information in non-equilibrium systems, (ii) the semiclassical energy-time quantization rule and (iii) the quasi-static information-energy correspondence, a new general rule for the quantization of quasi-static information states supported by an environment away from equilibrium is introduced if the history of the environment is known as a function of time in terms of its thermodynamic potential for information T ( t ) Δ S ( t ) that is a free energy measuring the distance from equilibrium Δ S ( t ) , and T ( t ) is the mean temperature of the environment at time t . This all new quasi-static information-time quantization rule is applied to the expanding Universe using a phenomenological thermodynamic potential for information in the matter-dominated era in order to find the eigen-information of the persistent structures that are supported by the universe (or the local environments therein) at any given epoch, thus providing an information–theoretic foundation for formation of structures and rise of complexity with time that embodies the cosmic evolution as epitomized by the late Wheeler’s famous conjecture ‘it from bit’. This theoretical procedure must also open new avenues for further research into the quantum theory of information and complexity in non-equilibrium thermodynamics.

Hagedorn temperature in holography: world-sheet and effective approaches

We provide general results on the Hagedorn temperature of planar, strongly coupled confining gauge theories holographically dual to type II superstring models on curved backgrounds with Ramond-Ramond and Kalb-Ramond fluxes and non-trivial dilaton. For exact backgrounds the Hagedorn temperature is determined up to next-to-next-to-next-to-leading order (NNNLO) in an expansion in α′; in all the other cases the results can be safely trusted up to NNLO. To reach these goals we exploit two complementary approaches. On the one hand, we perform an extrapolation to the Hagedorn regime of world-sheet results obtained from the semiclassical quantization of string configurations winding around the compact Euclidean time direction. En passant, we provide a detailed derivation of the fermionic part of the world-sheet spectrum, which is hard to find in the literature. On the other hand, we perturbatively solve the equations of motion for the thermal scalar field corresponding to the lightest mode of the winding string, which in flat space becomes tachyonic above the Hagedorn temperature. The interplay between different approaches is surely convenient, but we provide insights about a possible derivation of the whole NNLO correction to the Hagedorn temperature from a pure world-sheet perspective; furthermore, we determine the effective mass of the thermal scalar from the world-sheet in full generality.

Semi-Classical Limit and Quantum Corrections in Non-Coincidence Power-Law f(Q)-Cosmology

Semi-Classical Limit and Quantum Corrections in Non-Coincidence Power-Law f(Q)-Cosmology

Semiclassical Quantization Conditions in Strained Moiré Lattices

In this article we generalize the Bohr–Sommerfeld rule for scalar symbols at a potential well to matrix-valued symbols having eigenvalues that may coalesce precisely at the bottom of the well. As an application, we study the existence of approximately flat bands in moiré heterostructures such as strained two-dimensional honeycomb lattices in a model recently introduced by Timmel and Mele.

Using Lagrangian descriptors to calculate the Maslov index of periodic orbits.

The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of nonintegrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically demanding. In this paper, we describe a straightforward technique, for systems with two degrees of freedom, based on the Lagrangian descriptors. Our method is illustrated by applying it to the two-dimensional coupled quartic oscillator.

Vortex loop operators and quantum M2-branes

We study M2-branes in AdS_4× S^7/\mathbb{Z}_kAdS4×S7/ℤk dual to 1/2 and 1/3 BPS vortex loop operators in ABJM theory and compute their one-loop correction beyond the classical M2-brane action. The correction depends only on the parity of kk and is independent of all continuous parameters in the definition of the vortex loops. The result for odd kk agrees with the answers for the 1/2 BPS Wilson loop in the k=1k=1 theory and for even kk with the one in the k = 2k=2 theory. Combining with the classical part, we find that the natural expansion parameter seems to be 1/\sqrt{kN}1/kN rather than 1/\sqrt{N}1/N. This provides a further setting where semiclassical quantisation can be applied to M2-branes and produces new results inaccessible by other methods.

Semi-classical Pseudo-differential Operators on ħZn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar \\mathbb {Z}^n$$\\end{document} and Applications

In this paper we consider the semiclassical version of pseudo-differential operators on the lattice space ħZn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar {{\\mathbb {Z}}^{n}}$$\\end{document}. The current work is an extension of the previous work (Botchway et al. in J Funct Anal 278(11):108473, 33, 2020) and agrees with it in the limit of the parameter ħ→1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar \\rightarrow 1$$\\end{document}. The various representations of the operators will be studied as well as the composition, transpose, adjoint and the link between ellipticity and parametrix of operators. We also give the conditions for the ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell ^p$$\\end{document}, weighted ℓ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell ^2$$\\end{document} boundedness and ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell ^p$$\\end{document} compactness of operators. We investigate the relation between the classical and semi-classical quantization in the spirit of Ruzhansky and Turunen (Pseudo-differential operators and symmetries. Pseudo-differential operators, vol 2. Theory and Applications, Birkhäuser, Basel, 2010; J Fourier Anal Appl 16(6):943–982, 2010) RTspsJFAA and employ its applications to Schatten–von Neumann classes on ℓ2(ħZn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell ^2( \\hbar \\mathbb {Z}^n)$$\\end{document}. We establish Gårding and sharp Gårding inequalities, with an application to the well-posedness of parabolic equations on the lattice ħZn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar \\mathbb {Z}^n$$\\end{document}. Finally we verify that in the limiting case where ħ→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbar \\rightarrow 0$$\\end{document} the semi-classical calculus of pseudo-differential operators recovers the classical Euclidean calculus, but with a twist.

One-loop quantization of Euclidean D3-branes in holographic backgrounds

In this note we analyze the semi-classical quantization of D3-branes in three different holographic backgrounds in type IIB string theory. The first background is Euclidean AdS5 with S1× S3 boundary accompanied with a twist to preserve supersymmetry. We work out the spectrum of fluctuations around the classical D3-brane configuration, compute its one-loop partition function, and match to the non-perturbative correction to the superconformal index of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM. We then study Euclidean D3-branes in the Pilch-Warner geometry dual to the IR Leigh-Strassler fixed point of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1* with the aim to find non-perturbative corrections to its index. Finally we study Euclidean D3-branes in the non-geometric N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 J-fold background which is dual to the gauging of the 3D Gaiotto-Witten SCFT.

What Is the "Hydrogen Bond"? A QFT-QED Perspective.

In this paper we would like to highlight the problems of conceiving the "Hydrogen Bond" (HB) as a real short-range, directional, electrostatic, attractive interaction and to reframe its nature through the non-approximated view of condensed matter offered by a Quantum Electro-Dynamic (QED) perspective. We focus our attention on water, as the paramount case to show the effectiveness of this 40-year-old theoretical background, which represents water as a two-fluid system (where one of the two phases is coherent). The HB turns out to be the result of the electromagnetic field gradient in the coherent phase of water, whose vacuum level is lower than in the non-coherent (gas-like) fraction. In this way, the HB can be properly considered, i.e., no longer as a "dipolar force" between molecules, but as the phenomenological effect of their collective thermodynamic tendency to occupy a lower ground state, compatible with temperature and pressure. This perspective allows to explain many "anomalous" behaviours of water and to understand why the calculated energy associated with the HB should change when considering two molecules (water-dimer), or the liquid state, or the different types of ice. The appearance of a condensed, liquid, phase at room temperature is indeed the consequence of the boson condensation as described in the context of spontaneous symmetry breaking (SSB). For a more realistic and authentic description of water, condensed matter and living systems, the transition from a still semi-classical Quantum Mechanical (QM) view in the first quantization to a Quantum Field Theory (QFT) view embedded in the second quantization is advocated.

Geometric localization of waves on thin elastic structures.

We consider the localization of elastic waves in thin elastic structures with spatially varying curvature profiles, using a curved rod and a singly curved shell as concrete examples. Previous studies on related problems have broadly focused on the localization of flexural waves on such structures. Here, using the semiclassical WKB approximation for multicomponent waves, we show that in addition to flexural waves, extensional and shear waves also form localized, bound states around points where the absolute curvature of the structure has a minimum. We also see excellent agreement between our numerical experiments and the semiclassical results, which hinges on the vanishing of two extra phases that arise in the semiclassical quantization rule. Our findings open up novel ways to fine-tune the acoustic and vibrational properties of thin elastic structures and raise the possibility of introducing new phenomena not easily captured by effective models of flexural waves alone.

Chirp asymmetry as an analogue of leptogenesis

The effective conjugation symmetry that arises in the rotating wave frame is the analogue of the charge conjugation symmetry in field theory. Breaking this effective conjugation symmetry leads to asymmetries between up-chirped and down-chirped excitation in quantum optical systems. We use semiclassical quantum optics theory to describe these processes and experimentally characterize the asymmetry in the optical response in chirped, two-color saturated absorption spectroscopy (SAS) in an atomic vapor cell. Doing so demonstrates a theoretical and phenomenological correspondence to the simplest model of leptogenesis, the process by which our universe purportedly went from equal amounts of matter and antimatter to its present matter excess. The understanding of the asymmetry as due to a broken discrete symmetry under chirp illuminates the underlying processes responsible for other chirp asymmetries previously noted in the literature.

Semiclassical quantification of some two degree of freedom potentials: A differential Galois approach

In this work we explain the relevance of the Differential Galois Theory in the semiclassical (or WKB) quantification of some two degree of freedom potentials. The key point is that the semiclassical path integral quantification around a particular solution depends on the variational equation around that solution: a very well-known object in dynamical systems and variational calculus. Then, as the variational equation is a linear ordinary differential system, it is possible to apply the Differential Galois Theory to study its solvability in closed form. We obtain closed form solutions for the semiclassical quantum fluctuations around constant velocity solutions for some systems like the classical Hermite/Verhulst, Bessel, Legendre, and Lamé potentials. We remark that some of the systems studied are not integrable, in the Liouville–Arnold sense.

Analyzing quantum gravity spillover in the semiclassical regime

One of the standard approaches of incorporating the quantum gravity (QG) effects into the semiclassical analysis is to adopt the notion of a quantum-corrected spacetime arising from the QG model. This procedure assumes that the expectation value of the metric variable effectively captures the relevant QG subtleties in the semiclassical regime. We investigate the viability of this effective geometry approach for the case of dust dominated and a dark energy dominated universe. We write the phase space expressions for the geometric observables and construct corresponding Hermitian operators. A general class of operator ordering of these observables is considered, and their expectation values are calculated for a unitarily evolving wave packet. In the case of dust dominated universe, the expectation value of the Hubble parameter matches the “semiclassical” expression, the expression computed from the scale factor expectation value. In the case of the Ricci scalar, the relative difference between the semiclassical expression and quantum expectation is maximum at singularity and decays for late time. For a cosmological constant driven universe, the difference between the semiclassical expressions and the expectation value is most pronounced far away from the bounce point, hinting at the persistent quantum effect at the late time. The parameter related to the shape of the distribution appears as a control parameter in these models. In the limit of a sharply peaked distribution, the expectation value of the observables matches with their semiclassical counterpart, and the usage of effective geometry approach is justified.

A Prototype Method for the Detection and Recognition of Pigments in the Environment Based on Optical Property Simulation.

The possibility of pigment detection and recognition in different environments such as solvents or proteins is a challenging, and at the same time demanding, task. It may be needed in very different situations: from the nondestructive in situ identification of pigments in paintings to the early detection of fungal infection in major agro-industrial crops and products. So, we propose a prototype method, the key feature of which is a procedure analyzing the lineshape of a spectrum. The shape of the absorption spectrum corresponding to this transition strongly depends on the immediate environment of a pigment and can serve as a marker to detect the presence of a particular pigment molecule in a sample. Considering carotenoids as an object of study, we demonstrate that the combined operation of the differential evolution algorithm and semiclassical quantum modeling of the optical response based on a generalized spectral density (the number of vibronic modes is arbitrary) allows us to distinguish quantum models of the pigment for different solvents. Moreover, it is determined that to predict the optical properties of monomeric pigments in protein, it is necessary to create a database containing, for each pigment, in addition to the absorption spectra measured in a predefined set of solvents, the parameters of the quantum model found using differential evolution.

The Maslov index for composite power-law potentials: The case of the first Exton potential

Using the exact solution of the one-dimensional Schrödinger equation, we demonstrate that the Maslov index involved in the Bohr-Sommerfeld semiclassical quantization rule for the first Exton potential depends on the intensity parameters of the potential. As a function of the intensity of the potential term proportional to x−3/2, it varies within a rather wide range, from −1 to 0, adopting −1/6 when this term and its conjugate term ∼x−1, are absent, which is the case when the Exton potential reduces to the inverse-square-root potential.

Particle Trajectories for Quantum Maps

We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as defined by the propagation of a semiclassical defect measure. This convergence holds up to the Ehrenfest time of the classical system, which is larger when the system is “less chaotic.” In addition, we present numerical simulations of these effects. In proving this result, we provide a characterization of a type of semi-classical defect measure we call uniform defect measures. We also prove derivative estimates of a function composed with a flow on the torus.

Gaussian Decomposition vs. Semiclassical Quantum Simulation: Obtaining the High-Order Derivatives of a Spectrum in the Case of Photosynthetic Pigment Optical Properties Studying.

In this paper, a procedure for obtaining undistorted high derivatives (up to the eighth order) of the optical absorption spectra of biomolecule pigments has been developed. To assess the effectiveness of the procedure, the theoretical spectra of bacteriochlorophyll a, chlorophyll a, spheroidene, and spheroidenone were simulated by fitting the experimental spectra using the differential evolution algorithm. The experimental spectra were also approximated using sets of Gaussians to calculate the model absorption spectra. Theoretical and model spectra can be differentiated without smoothing (high-frequency noise filtering) to obtain high derivatives. Superimposition of the noise track on the model spectra allows us to obtain test spectra similar to the experimental ones. Comparison of the high derivatives of the model spectra with those of the test spectra allows us to find the optimal parameters of the filter, the application of which leads to minimal differences between the high derivatives of the model and test spectra. For all four studied pigments, it was shown that smoothing the experimental spectra with optimal filters makes it possible to obtain the eighth derivatives of the experimental spectra, which were close to the eighth derivatives of their theoretical spectra.

Fermions dynamic equation with Lorentz invariance violation and the corrected Hawking temperature in arbitrarily accelerating black hole* *Supported by the National Natural Science Foundation of China under Grant No. U2031121.

Containing Lorentz invariance violation (LIV), a new form of the fermions dynamic equation under the background of the curved space-time of the arbitrarily accelerating black hole, is studied. Firstly, we consider the new form of the fermions dynamic equation with arbitrary spin containing LIV in curved space-time, and research the fermions dynamic equation with spin containing LIV. On this basis, according to the semi-classical theory and black hole quantum tunneling radiation theory, the quantum tunneling radiation of the arbitrarily accelerating Kinnersly black hole is modified correctly, and the corrected physical quantities such as black hole temperature and quantum tunneling rate are deeply discussed. The fermions dynamic equation with arbitrary spin in the arbitrarily accelerating black hole space-time and its solution are explained in detail. In order to further obtain the correction effect of the Planck scale, this article considers beyond the semi-classical theory and further obtains new expressions of the black hole temperature and tunneling radiation rate.

Order-chaos transition in correlation diagrams and quantization of period orbits.

Eigenlevel correlation diagrams has proven to be a very useful tool to understand eigenstate characteristics of classically chaotic systems. In particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944 (1998)0031-900710.1103/PhysRevLett.80.944] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing the Planck constant, we induced a transition from order to chaos, in which scarred wave functions appeared as the interaction of pairs of eigenstates in broad avoided crossings, forming a well-defined frontier in the correlation diagram. In this paper, we demonstrate that this frontier can be obtained by means of the semiclassical quantization of the involved scarring periodic orbits. Additionally, in order to calculate the Maslov index of each scarring periodic orbit, which is necessary for the semiclassical quantization procedure, we introduce a straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.