Quantum Mechanical Evolution Research Articles

Black-hole Information Loss Problem: Past, Present, and Future

In this article, we discuss the information loss problem of black holes and critically review candidate resolutions of the problem. As a black hole evaporates via Hawking radiation, it seems to lose original quantum information; this indicates that the unitarity of time evolution in quantum mechanics and the fundamental predictability of physics are lost. We categorized candidate resolutions by asking (1) where information is and (2) which principle of physics is changed. We also briefly comment on the recent progress in the string theory community. Finally, we present several remarks for future perspectives.

Conformal quantum mechanics of causal diamonds

It is shown that a general radial conformal Killing vector in Minkowski space-time can be associated to a generator of time evolution in conformal quantum mechanics. Among these conformal Killing vectors there is a class which maps causal diamonds in Minkowski space-time into themselves. The flow of such Killing vectors describes worldlines of accelerated observers with a finite lifetime within a causal diamond. Time evolution of static diamond observers is equivalent to time evolution in conformal quantum mechanics governed by a hyperbolic Hamiltonian and covering only a segment of the time axis. This indicates that the Unruh temperature perceived by static diamond observers in the vacuum state of inertial observers in Minkowski space-time can be obtained from the behaviour of the two-point functions of conformal quantum mechanics. The results presented suggest a group theoretical description of the recently proposed light-cone temperature associated to null surfaces defined by light fronts in Minkowski space-time.

Multitime Landau–Zener model: classification of solvable Hamiltonians* * Authors made equal contributions to this article.

We discuss a class of models that generalize the two-state Landau–Zener Hamiltonian to both the multistate and multitime evolution. It is already known that the corresponding quantum mechanical evolution can be understood in great detail. Here, we present an approach to classify such solvable models, namely, to identify all their independent families for a given number N of interacting states and prove the absence of such families for some types of interactions. We also discuss how, within a solvable family, one can classify the scattering matrices, i.e., the system’s dynamics. Due to the possibility of such a detailed classification, the multitime Landau–Zener model defines a useful special function of theoretical physics.

Information geometry aspects of minimum entropy production paths from quantum mechanical evolutions.

We present an information geometric analysis of entropic speeds and entropy production rates in geodesic evolution on manifolds of parametrized quantum states. These pure states emerge as outputs of suitable su(2;C) time-dependent Hamiltonian operators used to describe distinct types of analog quantum search schemes. The Riemannian metrization on the manifold is specified by the Fisher information evaluated along the parametrized squared probability amplitudes obtained from analysis of the temporal quantum mechanical evolution of a spin-1/2 particle in an external time-dependent magnetic field that specifies the su(2;C) Hamiltonian model. We employ a minimum action method to transfer a quantum system from an initial state to a final state on the manifold in a finite temporal interval. Furthermore, we demonstrate that the minimizing (optimum) path is the shortest (geodesic) path between the two states and, in particular, minimizes also the total entropy production that occurs during the transfer. Finally, by evaluating the entropic speed and the total entropy production along the optimum transfer paths in a number of physical scenarios of interest in analog quantum search problems, we show in a clear quantitative manner that to a faster transfer there corresponds necessarily a higher entropy production rate. Thus we conclude that lower entropic efficiency values appear to accompany higher entropic speed values in quantum transfer processes.

Nanostructured material engineering for ultra-low loss MWIR thermal sensors – A short review

Evolution of quantum mechanics has brought a new-era of Infrared image sensing mechanisms. The energy efficient infrared thermal sensors are the most crucial requisite for realizing this on a low-cost, low-power technology platform. The demands for such low power on-chip sensors are approaching towards manipulating the light-matter interactions in a controlled manner. One of the most significant light-matter (photon and phonon) interactions, known as Brillouin phenomenon, could be an appropriate candidate to design the ultra-low loss mid-wave infrared (MWIR) thermal sensors. To control the brillouin interactions, advanced nanostructured materials with desired optomechanical properties required explorations. Such nanostructured materials have been engineered in a variety of ways to harness the opto-acoustic properties for ultra-low loss sensing applications. This work reviews the advancements in engineering the nanostructured materials using strong brillouin interactions, dedicated to ultra-low loss MWIR Thermal Sensors.

Transition probabilities in generalized quantum search Hamiltonian evolutions

A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schrödinger’s quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in detail the computational aspects necessary to calculate the transition probability from a source state to a target state in a continuous time quantum search problem defined by a multiparameter generalized time-independent Hamiltonian. In particular, quantifying the performance of a quantum search in terms of speed (minimum search time) and fidelity (maximum success probability), we consider a variety of special cases that emerge from the generalized Hamiltonian. In the context of optimal quantum search, we find it is possible to outperform, in terms of minimum search time, the well-known Farhi–Gutmann analog quantum search algorithm. In the context of nearly optimal quantum search, instead, we show it is possible to identify sub-optimal search algorithms capable of outperforming optimal search algorithms if only a sufficiently high success probability is sought. Finally, we briefly discuss the relevance of a tradeoff between speed and fidelity with emphasis on issues of both theoretical and practical importance to quantum information processing.

Path Integrals, Spontaneous Localisation, and the Classical Limit

Abstract The measurement problem and the absence of macroscopic superposition are two foundational problems of quantum mechanics today. One possible solution is to consider the Ghirardi–Rimini–Weber (GRW) model of spontaneous localisation. Here, we describe how spontaneous localisation modifies the path integral formulation of density matrix evolution in quantum mechanics. We provide two new pedagogical derivations of the GRW propagator. We then show how the von Neumann equation and the Liouville equation for the density matrix arise in the quantum and classical limit, respectively, from the GRW path integral.

Electromagnetic Gauge Choice for Scattering of\xa0Schr\xf6dinger Particle

We consider a Schrödinger particle placed in an external electromagnetic field of the form typical for scattering settings in the field theory: F=F^mathrm {ret}+F^mathrm {in}=F^mathrm {adv}+F^mathrm {out}, where the current producing F^{mathrm {ret}/mathrm {adv}} has the past and future asymptotes homogeneous of degree -3, and the free fields F^{mathrm {in}/mathrm {out}} are radiation fields produced by currents with similar asymptotic behavior. We show that with appropriate choice of electromagnetic gauge the particle has ‘in’ and ‘out’ states reached with no further modification of the asymptotic dynamics. We use a special quantum mechanical evolution ‘picture’ in which the free evolution operator has well-defined limits for trightarrow pm infty , and thus the scattering wave operators do not need the free evolution counteraction. The existence of wave operators in this setting is established, but the proof of asymptotic completeness is not complete: more precise characterization of the asymptotic behavior of the particle for |mathbf {x}|=|t| would be needed.

Beyond Superconductivity

We present a novel device concept that utilizes the fascinating transition regime between quantum mechanics and classical physics. The devices operate by using a small number of individual quantum mechanical collapse events to interrupt the unitary evolution of quantum states represented by wave packets. Exceeding the constraints of the unitary evolution of quantum mechanics given by Schrödinger’s equation and of classical Hamiltonian physics, these devices display a surprising behavior.

WKB Asymptotics and Spectral Deformation in Semi-classical Limit

Phase-integral method is applied to study semi-classical limit for the spectral problem related to dynamical system describing quantum mechanical evolution with space-time reflection symmetry. The main goal of the paper is to investigate the relationship between analytic properties of the corresponding potential and the structure of limiting spectral graph. Quantization conditions of Bohr-Sommerfeld type are derived specifying localization of the spectrum for the model problem with a one-parameter family of polynomial potentials treated as deformation of a linear one.

Non-equilibrium relaxation of hot states in organic semiconductors: Impact of mode-selective excitation on charge transfer.

The theoretical study of open quantum systems strongly coupled to a vibrational environment remains computationally challenging due to the strongly non-Markovian characteristics of the dynamics. We study this problem in the case of a molecular dimer of the organic semiconductor tetracene, the exciton states of which are strongly coupled to a few hundreds of molecular vibrations. To do so, we employ a previously developed tensor network approach, based on the formalism of matrix product states. By analyzing the entanglement structure of the system wavefunction, we can expand it in a tree tensor network state, which allows us to perform a fully quantum mechanical time evolution of the exciton-vibrational system, including the effect of 156 molecular vibrations. We simulate the dynamics of hot states, i.e., states resulting from excess energy photoexcitation, by constructing various initial bath states, and show that the exciton system indeed has a memory of those initial configurations. In particular, the specific pathway of vibrational relaxation is shown to strongly affect the quantum coherence between exciton states in time scales relevant for the ultrafast dynamics of application-relevant processes such as charge transfer. The preferential excitation of low-frequency modes leads to a limited number of relaxation pathways, thus "protecting" quantum coherence and leading to a significant increase in the charge transfer yield in the dimer structure.

Quantum non-linear evolution of inflationary tensor perturbations

We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions. We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes. Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time. The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describes the quantum-to-classical transition of the tensor perturbations. This is different from the classicality accomplished by the squeezed state, the suppression of the non-commutative effect, which is originated from the quadratic, linear interaction, and also maintains the unitarity. The quantum-to-classical transition occurs within 5–10 e-folds, faster than the curvature perturbation.

Fractional evolution in quantum mechanics

Fractional time (non-unitary) quantum mechanics is discussed for both Schrödinger and Heisenberg representations of quantum mechanics. A correct form of the fractional Schrödinger equation is elucidated. A generic regularization procedure for the fractional Heisenberg equations of motion is suggested that makes it possible to solve these nonlinear equations in the framework of photonic and spin coherent states consideration.

Bloch-Messiah decomposition and Magnus expansion for parametric down-conversion with monochromatic pump

We discuss the Bloch-Messiah decomposition for the broadband squeezed light generated by type-I parametric down-conversion with monochromatic pump. Using an exact solution for this process, we evaluate the squeezing parameters and the corresponding squeezing eigenmodes. Next, we consider the Magnus expansion of the quantum-mechanical evolution operator for this process and obtain its first three approximation orders. Using these approximated solutions, we evaluate the corresponding approximations for the Bloch-Messiah decomposition. Our results allow us to conclude that the first-order approximation of the Magnus expansion is sufficient for description of the broadband squeezed light for squeezing values below 12.5 dB. For higher degrees of squeezing we show fast convergence of the Magnus series providing a good approximation for the exact solution already in the third order. We propose a quantitative criterion for this ultra-high-gain regime of parametric down-conversion when the higher-orders terms of the Magnus expansion, known in the literature as the operator-ordering effects, become necessary.

Imagery, intuition and imagination in quantum physics education

In response to the authors, I demonstrate how threshold concepts offer a means to both contextualise teaching and learning of quantum physics and help transform students into the culture of physics, and as a way to identify particularly troublesome concepts within quantum physics. By drawing parallels from my own doctoral research in another area of contemporary physics—special relativity—I highlight concepts that require an ontological change, namely a shift beyond the reality of everyday Newtonian experience such as time dilation and length contraction, as being troublesome concepts that can present barriers to learning with students often asking “is it real?”. Similarly, the domain of quantum physics requires students to move beyond “common sense” perception as it brings into sharp focus the difference between what is experienced via the sense perceptions and the mental abstraction of phenomena. And it’s this issue that highlights the important role imagery and creativity have both in quantum physics and in the evolution of physics more generally, and lies in stark contrast to the apparent mathematical focus and lack of opportunity for students to explore ontological issues evident in the authors’ research. By reflecting on the authors’ observations of a focus on mathematical formalisms and problem solving at the expense of alternative approaches, I explore the dialectic between Heisenberg’s highly mathematical approach and Schrodinger’s mechanical wave view of the atom, together with its conceptual imagery, at the heart of the evolution of quantum mechanics. In turn, I highlight the significance of imagery, imagination and intuition in quantum physics, together with the importance of adopting an epistemological pluralism—multiple ways of knowing and thinking—in physics education. Again drawing parallels with the authors’ work and my own, I identify the role thought experiments have in both quantum physics education and in physics more generally. By introducing the notion of play, I advocate adopting and celebrating multiple approaches of teaching and learning, including thought experiments, play, dialogue and a more conceptual approach inclusive of multiple forms of representation, that complements the current instructional, mathematical approach so as to provide better balance to learning, teaching and the curriculum.

NON-UNITARY TRANSFORMATION OF QUANTUM TIME-DEPENDENT NON-HERMITIAN SYSTEMS

We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary transformation and the associated evolution, and collecting the basic results around it and postulating the norm preserving. This cautionary postulate imposing that the time evolution of a non Hermitian quantum system preserves the inner products between the associated states must not be read naively. We also give an example showing that the solutions of time-dependent non Hermitian Hamiltonian systems given by a linear combination of SU(1,1) and SU(2) are obtained thanks to time-dependent non-unitary transformation.

Information transport in classical statistical systems

For “static memory materials” the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics – such materials are “quantum simulators”. For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Quantum versus classical dynamics in the optical centrifuge

The interplay between classical and quantum-mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum-mechanical formalism starting from either the ground state or a thermal ensemble. Two resonant mechanisms are identified, i.e., the classical autoresonance and the quantum-mechanical ladder climbing, yielding different dynamics and rotational excitation efficiencies. The rotating-wave approximation is used to analyze the two resonant regimes in the associated dimensionless two-parameter space and calculate the OC excitation efficiency. The results show good agreement between numerical simulations and theory and are relevant to existing experimental setups.

Efficient solution of the Wigner–Liouville equation using a spectral decomposition of the force field

The Wigner–Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner–Liouville kernel both conceptually and numerically as the spectral force Wigner–Liouville equation avoids the numerical evaluation of the highly oscillatory Wigner kernel which is nonlocal in both position and momentum. The quantum mechanical evolution is instead governed by a term local in space and non-local in momentum, where the non-locality in momentum has only a limited range. An interpretation of the time evolution in terms of two processes is presented; a classical evolution under the influence of the averaged driving field, and a probability-preserving quantum-mechanical generation and annihilation term. Using the inherent stability and reduced complexity, a direct deterministic numerical implementation using Chebyshev and Fourier pseudo-spectral methods is detailed. For the purpose of illustration, we present results for the time-evolution of a one-dimensional resonant tunneling diode driven out of equilibrium.

Quantum interference of position and momentum: A particle propagation paradox

Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time t. Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within the respective position and momentum intervals. These violations of the particle propagation inequality show that quantum mechanics changes the laws of motion at a fundamental level, providing a new perspective on causality relations and time evolution in quantum mechanics.