Quantum Mechanical Theory Research Articles

A symmetry principle for emergent spacetime

There are many examples where geometry and gravity are concepts that emerge from a theory of quantum mechanics without gravity. This suggests thinking of gravity as an exotic phase of matter. Quantifying this phase in the Landau paradigm requires some sort of symmetry principle or order parameter that captures its appearance. In this essay, we propose higher-form symmetries as a symmetry principle underlying emergent spacetime. We explore higher-form symmetries in gauge–gravity duality and explain how their breaking describes features of gravitational theory. Such symmetries imply the existence of nonlocal objects in the gravitational theory — in gauge–gravity duality these are the strings and branes of the bulk theory — giving an alternative way to understand the nonlocality necessary in any ultraviolet completion of gravity.

What can bouncing oil droplets tell us about quantum mechanics?

A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be induced to display a number of behaviours previously considered to be distinctly quantum. To explain this correspondence it has been suggested that the fluid mechanical system provides a single-particle classical model of de Broglie’s idiosyncratic ‘double solution’ pilot wave theory of quantum mechanics. In this paper we assess the epistemic function of the bouncing oil droplet experiments in relation to quantum mechanics. We find that the bouncing oil droplets are best conceived as an analogue illustration of quantum phenomena, rather than an analogue simulation, and, furthermore, that their epistemic value should be understood in terms of how-possibly explanation, rather than confirmation. Analogue illustration, unlike analogue simulation, is not a form of ‘material surrogacy’, in which source empirical phenomena in a system of one kind can be understood as ‘standing in for’ target phenomena in a system of another kind. Rather, analogue illustration leverages a correspondence between certain empirical phenomena displayed by a source system and aspects of the ontology of a target system. On the one hand, this limits the potential inferential power of analogue illustrations, but, on the other, it widens their potential inferential scope. In particular, through analogue illustration we can learn, in the sense of gaining how-possibly understanding, about the putative ontology of a target system via an experiment. As such, the potential scientific value of these extraordinary experiments is undoubtedly a significant one.

Atomistic-Benchmarking towards a protocol development for rapid quantitative metrology of piezoelectric biomolecular materials

Biomolecular crystals are an emerging class of piezoelectric materials that are both biocompatible and biodegradable, which enables their use in biomedical applications and smart devices while ensuring eco-friendly production and disposal. However, accurate quantification of the piezoelectric response of soft sub-micron crystals remains a significant challenge, as conventional piezoelectric measurement techniques are suited to ceramics, thin films, and polymers. Here, we demonstrate the use of a novel piezoresponse force microscopy (PFM) methodology for robust, reliable quantification of the electromechanical response of biomolecular crystals. As a strong test of high accuracy and precision, we show that PFM, integrated with quantum mechanical (QM) density functional theory (DFT) calculations, can distinguish the piezoelectric responses of near-isopiezoelectric amino acid crystals. We show that a statistical approach, combined with experimental best practices, provides effective piezoelectric coefficients of biomolecular single crystals accurately and unambiguously. This work opens the door to high-throughput screening and characterisation of natural and engineered soft piezoelectric crystals for eco-friendly energy harvesters and biodegradable medical implants, reducing dependence on lead-based and rare-earth-containing piezoelectric materials.

Harvesting of surface plasmon polaritons: Role of the confinement factor.

Surface plasmon polaritons (SPPs) are propagating waves generated at the interface of a metal (metamaterial) and a dielectric. The intensity of SPPs often exponentially decays away from the surface, while their wavelengths can be tuned by the confinement effect. We present here a computational method based on quantum-mechanical theory to fully describe the interaction between confined SPPs and adsorbed molecules at the interface. Special attention has been paid to the roles of the confinement factor. Taking a prototype dye sensitized solar cell as an example, calculated results reveal that with the increase in the confinement factor in metal/dielectric interfaces, the breakdown of the conventional dipole approximation emerges, which allows efficient harvesting of SPPs with low excitation energies and, thus, increases the efficiency of the solar energy conversion by dye molecules. Furthermore, at the metamaterial/dielectric interface, SPPs with large confinement factors could directly excite the dye molecule from its ground singlet state to the triplet state, opening an entirely new channel with long-living carriers for the photovoltaic conversion. Our results not only provide a rigorous theory for the SPP-molecule interaction but also highlight the important role played by the momentum of the light in plasmon related studies.

Effects of entanglement on vortex dynamics in the hydrodynamic representation of quantum mechanics

The hydrodynamic representation of quantum mechanics describes virtual flow as if a quantum system were fluid in motion. This formulation illustrates pointlike vortices when the phase of a wavefunction becomes nonintegrable at nodal points. We study the dynamics of such pointlike vortices in the hydrodynamic representation for a two-particle wavefunction. In particular, we discuss how quantum entanglement influences vortex–vortex dynamics. For this purpose, we employ the time-dependent quantum variational principle combined with the Rayleigh–Ritz method. We analyze the vortex dynamics and establish connections with Dirac’s generalized Hamiltonian formalism.

Schrödinger Equation for Energy Levels as a Linear Equation for Probability Distributions Identified with Quantum States

In this paper, we show that the energy spectrum of a qudit system (spin-j, N-level atom) with Hamiltonian N×N matrix H is determined by the equation for eigenvalues of the N2×N2 matrix ℋ and its eigenvectors | p⟩ with components, which are probability distributions identified with quantum states in the probability representation of quantum mechanics. We derive this equation based on the conventional Schrodinger equation for the state vector | ψ⟩. We discuss the example of qubit in detail and study new entropic characteristics of the energy levels.

Precision spectroscopy of atomic helium.

Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the ‘proton radius puzzle’. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.

Hamiltonian deformations in quantum mechanics, TT¯ , and the SYK model

Motivated by $T\bar T$, we introduce and study a wide class of solvable deformations of quantum-mechanical theories. These deformations map the Hamiltonian to a function of itself. We solve these theories by computing all finite-temperature correlation functions of the deformed theory in terms of the correlators of the undeformed theory. Applications to AdS/CFT, SYK, and the Schwarzian theory are considered. We write down the deformed Schwarzian action for an arbitrary Hamiltonian deformation and find that the maximal Lyapunov exponent is unchanged.

On the origin of the weak equivalence principle in a theory of emergent quantum mechanics

We argue that in a framework for emergent quantum mechanics, the weak equivalence principle is a consequence of concentration of measure in large-dimensional spaces of [Formula: see text]-Lipshitz functions. Furthermore, as a consequence of the emergent framework and the properties that we assume for the fundamental dynamics, it is argued that gravity must be a classical, emergent interaction.

Transgression of Concepts of Natural Knowledge in Social Process

Introduction. The problem of the search for the ways of understanding of the picture of the world and, as a consequence, the development of an approach to the social management is relevant for all times of the existence of mankind. A human is basically a biological phenomenon, therefore, the natural order should be regarded as the basis of the social order. Having in mind this formulation of the question, it becomes necessary to analyze modern concepts of natural science in understanding not only ontological vision of human society, but also developing new ways of its understanding. Materials and Methods. The theoretical and methodological approach was based on the concepts of natural science including the theories of evolutionism, quantum mechanics and synergetics. Using the model transfer of these theories to the idea of social development, the author proposes the methodology based on the principle of interdependence of the theories analyzed in the article. Results. An analysis within the framework of the described theories has shown that according to the evolutionary model, progress is assumed to be taken for granted. Linear scenarios are useful only at the stage of forecasting and provoke a passivity of existence, which leads to deadlocks in development. In the synergetic model, society is represented as a complex open system characterized by opposite trends: destruction, manifesting itself as entropy, and creation, or negentropy. Progress depends on changes that help to survive. If the synergistic picture of the world appears in the form of an order that is formed from chaos, then in a quantum one – society is chaos in the originally existing order. Consequently, the presence of a goal-oriented vector compels a person to move towards the restoration of the system, in particular society, to its initial or even higher level of organization. Discussion and Conclusion. A progressive evolutionary model is manifested in the form of successful adaptation, synergetic combines the idea of evolutionism with the idea of multivariance of the historical process. The quantum approach continues the idea of multivariance, but unlike classical synergetics, it assumes a goal-oriented nature of development. In fact, these approaches do not express contradiction, but the disclosure of the multidimensional development of being, therefore, it is necessary to take into account their interdependence, which allows a more productive cognition of reality in order to manage it.

Relationship between molecular charge distribution and wettability reversal efficiency of cationic surfactants on calcite surfaces

Wettability reversal is a critical factor in enhanced oil recovery (EOR) from predominantly oil-wet carbonate reservoirs. Cationic surfactants are able to efficiently reverse carbonate wettability due to their electrostatic interactions with the surface adsorbed carboxylate (acidic) components of the crude oil. However, details concerning the relationship between the surfactant molecular structures and their wettability alteration efficiency are lacking. In this study, we systematically probe the effect of the molecular charge distribution of quaternary ammonium type cationic surfactants on the wettability reversal efficiency. The local charges on the hydrophilic head group of the surfactants were varied by insertion of different functional groups and the charge distribution was calculated using quantum mechanical density functional theory (DFT) method. Ten modified surfactants as well as the reference octyltrimethylammonium molecule were tested using the molecular dynamics (MD) simulations. The results imply that the charge on the hydrogen atoms in the methylene group of a quaternary ammonium moiety has the most significant influence on the wettability reversal ability of the surfactants, with the Spearman rank coefficient (ρ) being as high as 0.782, while charges on the quaternary ammonium group as a whole do not pose any considerable effect, with ρ being −0.264. The calculations further suggest some feasible chemical modifications of the surfactants leading to the highest wettability alteration efficiency (i.e., insertion of a ketone group). Additionally, the effect of alkyl chain length was explored and an optimal length was identified that suggests the importance of establishing the structural compatibility between the surfactants and the oil phase. The correlations obtained in this study can facilitate the design of high-efficiency cationic surfactants for wettability reversal in carbonate reservoirs.

Energy loss by relativistic electron ensembles due to coherent excitation and ionization of atoms

Coherent effects in the ionization loss of ultrarelativistic electron ensembles (bunches) are studied on the basis of perturbation theory of quantum mechanics. These effects originate from the interference of the electrons' proper electric fields with each other. General expressions for the ionization loss in this case, as well as their applicability conditions, are derived. It is shown that for ensembles of sufficiently small spatial size, achievable in modern accelerator facilities, the discussed effects lead to an increase of the ionization loss by several orders of magnitude compared to the result predicted by the Bethe-Bloch formula. In this case, the effective mean ionization potentials of the atomic shells depend not only on the structure of the atomic levels, but on the ensemble form factors as well. The numerical calculations are made for hydrogen atoms, taking into account the density effect in the ionization loss. The ionization loss due to resonant excitation and ionization of atoms by ensembles with periodical modulation of the particle density (realized at free-electron lasers) is investigated.

Probability Representation of Quantum Mechanics and the Quantizer—Dequantizer Formalism

A review of the approach where the states of quantum systems are identified with fair probability distributions is presented. The quantizer–dequantizer operators used to construct the invertible map of the density operators onto the probability distributions are applied to obtain the kinetic equations for probability distributions identified with the quantum system states. For qubit states, the von Neumann evolution equation for the density operator is explicitly given in the form of kinetic equation for the probability distribution. Simplest tomographic probability distributions describing the states of multimode quantum oscillator are constructed.

Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma.

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive abinitio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (<50 eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50eV, while producing stable molecular dynamics and accurate diffusion coefficients.

Machine Learning for Accurate Force Calculations in Molecular Dynamics Simulations.

The computationally expensive nature of ab initio molecular dynamics simulations severely limits its ability to simulate large system sizes and long time scales, both of which are necessary to imitate experimental conditions. In this work, we explore an approach to make use of the data obtained using the quantum mechanical density functional theory (DFT) on small systems and use deep learning to subsequently simulate large systems by taking liquid argon as a test case. A suitable vector representation was chosen to represent the surrounding environment of each Ar atom, and a Δ-NetFF machine learning model, where the neural network was trained to predict the difference in resultant forces obtained by DFT and classical force fields, was introduced. Molecular dynamics simulations were then performed using forces from the neural network for various system sizes and time scales depending on the properties we calculated. A comparison of properties obtained from the classical force field and the neural network model was presented alongside available experimental data to validate the proposed method.

Single-shot temporal characterization of XUV pulses with duration from ∼10 fs to ∼350 fs at FLASH

Ultra-short extreme ultraviolet pulses from the free-electron laser FLASH are characterized using terahertz-field driven streaking. Measurements at different ultra-short extreme ultraviolet wavelengths and pulse durations as well as numerical simulations were performed to explore the application range and accuracy of the method. For the simulation of streaking, a standard classical approach is used which is compared to quantum mechanical theory, based on strong field approximation. Various factors limiting the temporal resolution of the presented terahertz streaking setup are investigated and discussed. Special attention is paid to the cases of very short (∼10 fs) and long (up to ∼350 fs) pulses.

SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics

In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the S U ( 2 ) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random variables. The dichotomic random variables are spin-1/2 particle projections m = ± 1 / 2 onto three perpendicular directions in the space. The invertible maps of qubit density operators onto fair probability distributions are constructed. In the suggested probability representation of quantum states, the Schrödinger and von Neumann equations for the state vectors and density operators are presented in explicit forms of the linear classical-like kinetic equations for the probability distributions of random variables. The star-product and quantizer–dequantizer formalisms are used to study the qubit properties; such formalisms are discussed for photon tomographic probability distribution and its correspondence to the Heisenberg–Weyl symmetry properties.

Non-degenerate fourth order perturbation theory

There exist several forms of perturbation theory in Quantum Mechanics, namely: non-degenerate perturbation theory, degenerate perturbation theory, time-dependent perturbation theory, time-constant perturbation theory and time-harmonic perturbation theory. This paper presents an extension of the perturbation theory for non-degenerate states. It has been observed that most texts and journal papers treat only the first –order and second-order non-degenerate perturbation theory. Therefore, this paper attempts to treat and present the third order and fourth order non-degenerate perturbation theory in quantum mechanics. It can thus be asserted that the higher the order of perturbations of quantum systems that we know, the more successful will be our efforts in suppressing or eliminating them.

Method for Accurately Predicting Solvation Structure.

Accurately predicting the molecular structure of solutions is a fundamental scientific challenge. Using quantum mechanical density functional theory (DFT) to make these predictions is hindered by significant variation depending on which DFT functional is used. Here, we present a simple metric that can determine the reliability of a DFT functional for predicting solvation structure. We then show that including a simple interaction term to correct this metric leads to quantitative agreement with experimental measurements of liquid structure. We demonstrate the utility of this method by using it to accurately describe the hydration structure around the Na+ and K+ ions as well as the structural properties of pure water with a computationally cheap functional.

Implementation of quantum teleportation of photons across an air – water interface

Since the theory of quantum mechanics brought about a revolution in physics nearly a century ago, various applications have emerged. In particular, the quantum properties of photons are being studied to provide a solution to some of the challenges faced by existing communication networks, such as security issues and energy efficiency. One of these properties is teleportation, via which information regarding the state of a photon, without its physical motion, can be transmitted across a classical channel. We report, perhaps for the first time, the teleportation of photons across a simulated air–water interface. An entangled pair of photons is generated from a mode-locked laser source, through spontaneous four-wave mixing (SFWM). One of the pair is sent wirelessly to an underwater receiver. Six States of Polarization are teleported sequentially, implementing active feed-forward operation, with the average fidelity of 96.7% surpassing the classical limit. This work is anticipated to lead to the establishment of a quantum communication link between two different media.