Unified Quantum Research Articles

Glide and Superclimb of Dislocations in Solid 4He

Glide and climb of quantum dislocations under finite external stress, variation of chemical potential and bias (geometrical slanting) in Peierls potential are studied by Monte Carlo simulations of the effective string model. We treat on unified ground quantum effects at finite temperatures $T$. Climb at low $T$ is assisted by superflow along dislocation core -- {\it superclimb}. Above some critical stress avalanche-type creation of kinks is found. It is characterized by hysteretic behavior at low $T$. At finite biases gliding dislocation remains rough even at lowest $T$ -- the behavior opposite to non-slanted dislocations. In contrast to glide, superclimb is characterized by quantum smooth state at low temperatures even for finite bias. In some intermediate $T$-range giant values of the compressibility as well as non-Luttinger type behavior of the core superfluid are observed.

Quantum mechanics flummoxes physicists again

A fresh take on a classic experiment makes no progress in unifying quantum mechanics and relativity.

Unified quantum jump superoperator for optical fields from the weak- to the strong-coupling limit

We derive a generalized quantum jump superoperator that can be used in the quantum trajectory description of single photon detectors, light-emitting diodes (LEDs), and lasers. Our model describes an optical single-mode cavity field coupled to a reservoir through a two-state quantum system and includes three physical parameters: the coupling of the field to the two-state system, the coupling of the two-state system to the reservoir, and the cavity loss rate. In this setup, the two-state system can act as a photodetector or as an energy-adding mechanism. In the first case, we assume that the reservoir acts as a damping mechanism for an ideal cavity and derive reduced field operators describing the photon detection events. Our model coincides with the commonly known quantum trajectory based photon counting models at the weak- and strong-coupling limits and is, furthermore, also applicable between their validity regimes. In the second case, we assume that the reservoir injects energy into a lossy cavity through the two-state system. Again we derive the reduced field operators describing photon creation events into the lossy cavity. We show that this setup can act as an LED or as a laser depending on the strength of the injection. We also investigatemore » how the setup operates at the close proximity of the lasing threshold.« less

Postponing the Past: An Operational Analysis of Delayed-Choice Experiments

The prominent characteristic of a delayed-choice effect is to make the choice between complementary types of phenomena after the relevant interaction between the system and measuring instrument has already come to an end. In this paper, we first represent a detailed comparative analysis of some early delayed-choice propositions and also most of the experimentally performed delayed-choice proposals in a coherent and unified quantum mechanical formulation. Taking into the account the represented quantum mechanical descriptions and also the rules of probability theory, we discuss that there are two fundamentally different descriptions concerning the physical mechanism of the delayed-choice between the complementary types of phenomena in these experiments. In this regard, we finally conclude that the delayed-choice experiments can be classified into two main groups where the temporal aspect of each group is characterized differently within their probabilistic descriptions.

A unified quantum NOT gate

We study the universal quantum NOT machine (approximate) when the quantum state lies between two latitudes on the Bloch sphere and present an analytical formula for the optimized 1-to-M quantum NOT gate. Our result generalizes previous results concerning a quantum NOT gate for a quantum state distributed uniformly on the whole Bloch sphere as well as for the phase-covariant quantum state. We have also shown that such a 1-to-M optimized NOT gate can be implemented using a sequential generation scheme via matrix product states.

Relation of a unified quantum field theory of spinors to the structure of general relativity

Based on a unified quantum field theory of spinors assumed to describe all matter fields and their interactions we construct the space-time structure of general relativity according to a general connection within the corresponding spinor space. The tetrad field and the corresponding metric field are composed from a space-time dependent basis of spinors within the internal space of the fundamental matter field. Similar to twistor theory the Minkowski signature of the space-time metric is related to this spinor nature of elementary matter, if we assume the spinor space to be endowed with a symplectic structure. The equivalence principle and the property of background independence arise from the fact that all elementary fields are composed from the fundamental spinor field. This means that the structure of space-time according to general relativity seems to be a consequence of a fundamental theory of matter fields and not a presupposition as in the usual setting of relativistic quantum field theories.

Noncommutative closed Friedman universe

Heller et al. (J Math Phys 46:122501, 2005; Int J Theor Phys 46:2494, 2007) proposed a model unifying general relativity and quantum mechanics based on a noncommutative algebra \({\mathcal{A}}\) defined on a groupoid having the frame bundle over space–time as its base space. The generalized Einstein equation is assumed in the form of the eigenvalue equation of the Einstein operator on a module of derivations of the algebra \({\mathcal{A}}\) . No matter sources are assumed. The closed Friedman world model, when computed in this formalism, exhibits two interesting properties. First, generalized eigenvalues of the Einstein operator reproduce components of the perfect fluid energy-momentum tensor for the usual Friedman model together with the corresponding equation of state. One could say that, in this case, matter is produced out of pure (noncommutative) geometry. Second, owing to probabilistic properties of the model, in the noncommutative regime (on the Planck level) singularities are irrelevant. They emerge in the process of transition to the usual space–time geometry. These results are briefly discussed.

AN OPERATIONAL ALGEBRAIC APPROACH TO QUANTUM CHANNEL CAPACITY

An elementary introduction into algebraic approach to unified quantum information theory and operational approach to quantum entanglement as generalized encoding is given. After introducing compound quantum state and two types of informational divergences, namely, Araki–Umegaki (a-type) and of Belavkin–Staszewski (b-type) quantum relative entropic information, this paper treats two types of quantum mutual information via entanglement and defines two types of corresponding quantum channel capacities as the supremum via the generalized encodings. It proves the additivity property of quantum channel capacities via entanglement, which extends the earlier results of Belavkin to products of arbitrary quantum channels for quantum relative entropy of any type.

Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion

For every rational homology $3$-sphere with $H_1(M,\mathbb Z) =(\mathbb Z/2\mathbb Z)^n$ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd

COSMOLOGICAL DEFECT AND HIGH ENERGY EXPERIMENTS

The production and evolution of cosmological defects are investigated based on the standard particle physics theory such as the electroweak unified model and quantum chromodynamics. In these models, the string type solution can be obtained. Although electroweak strings and pion strings are embedded ones and topologically unstable, they would be stabilized by high temperature plasma and bring various cosmological consequences. Moreover, the production of pion strings may be observed in the LHC experiment.

General entanglement-assisted quantum error-correcting codes

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs, which can only be constructed from dual-containing codes. Operator quantum error-correcting codes allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum error-correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.

Symmetries and polarization correlations in collision processes

A unified quantum collision theory for an elementary reaction is reviewed in the wave-packet approach. General kinematic analyses of various atomic collision processes by using the density-matrix and helicity formulations are presented. The rotation, parity, and time-reversal symmetries of the colliding system are considered. In addition to polarization and angular correlations in each collision process, correspondences among different collision processes are also studied. These symmetry studies in atomic collisions provide a great deal of valuable information about the colliding systems and enhances our knowledge on the collision dynamics.

Conceptual Unification of Gravity and Quanta

We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra \mbox{\cal A} on the groupoid \Gamma = E \times G where E is the total space of the frame bundle over spacetime, and G the Lorentz group. The differential geometry, based on derivations of \mbox{\cal A}, is constructed. The eigenvalue equation for the Einstein operator plays the role of the generalized Einstein's equation. The algebra \mbox{\cal A}, when suitably represented in a bundle of Hilbert spaces, is a von Neumann algebra \mathcal{M} of random operators representing the quantum sector of the model. The Tomita-Takesaki theorem allows us to define the dynamics of random operators which depends on the state \phi . The same state defines the noncommutative probability measure (in the sense of Voiculescu's free probability theory). Moreover, the state \phi satisfies the Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a generalized equilibrium state. By suitably averaging elements of the algebra \mbox{\cal A}, one recovers the standard geometry of spacetime. We show that any act of measurement, performed at a given spacetime point, makes the model to collapse to the standard quantum mechanics (on the group G). As an example we compute the noncommutative version of the closed Friedman world model. Generalized eigenvalues of the Einstein operator produce the correct components of the energy-momentum tensor. Dynamics of random operators does not ``feel'' singularities.

Unified quantum description of TRI and ROT effects in ternary fission

It is shown that consideration of the Coriolis interaction makes it possible to explain both T-odd effects observed in ternary fission induced by polarized neutrons. A possible reason for the difference in the effects observed for 233U and 235U targets is discussed.

Unifying Quantum State Transfer and State Amplification

We present a Hamiltonian that can be used for amplifying the signal from a quantum state, enabling the measurement of a macroscopic observable to determine the state of a single spin. We prove a general mapping between this Hamiltonian and an exchange Hamiltonian for arbitrary coupling strengths and local magnetic fields. This facilitates the use of existing schemes for perfect state transfer to give perfect amplification. We further prove a link between the evolution of this fixed Hamiltonian and classical cellular automata, thereby unifying previous approaches to this amplification task. Finally, we show how to use the new Hamiltonian for perfect state transfer in the scenario where total spin is not conserved during the evolution, and demonstrate that this yields a significantly different response in the presence of decoherence.

Time Flow in a Noncommutative Regime

We develop an approach to dynamical and probabilistic properties of the model unifying general relativity and quantum mechanics, initiated in the paper (Heller et al. (2005) International Journal Theoretical Physics44, 671). We construct the von Neumann algebra \({\cal M}\) of random operators on a groupoid, which now is not related to a finite group G, but is the pair groupoid of the Lorentzian frame bundle E over spacetime M. We consider the time flow on \({\cal M}\) depending on the state \(\phi \). The state \(\phi \) defining the noncommutative dynamics is assumed to be normal and faithful. Then the pair \(({\cal M}, \phi) \) is a noncommutative probabilistic space and \(\phi\) can also be interpreted as an equilibrium thermal state, satisfying the Kubo-Martin-Schwinger condition. We argue that both the “time flow” and thermodynamics have their common roots in the noncommutative unification of dynamics and probability.

New ‘phase’ of quantum gravity

The emergence of loop quantum gravity over the past two decades has stimulated a great resurgence of interest in unifying general relativity and quantum mechanics. Among a number of appealing features of this approach is the intuitive picture of quantum geometry using spin networks and powerful mathematical tools from gauge field theory. However, the present form of loop quantum gravity suffers from a quantum ambiguity, owing to the presence of a free (Barbero-Immirzi) parameter. Following the recent progress on conformal decomposition of gravitational fields, we present a new phase space for general relativity. In addition to spin-gauge symmetry, the new phase space also incorporates conformal symmetry making the description parameter free. The Barbero-Immirzi ambiguity is shown to occur only if the conformal symmetry is gauge fixed prior to quantization. By withholding its full symmetries, the new phase space offers a promising platform for the future development of loop quantum gravity. This paper aims to provide an exposition, at a reduced technical level, of the above theoretical advances and their background developments. Further details are referred to cited references.

Teaching the Quantal Exposition of the Unified Quantum Theory of Mechanics and Thermodynamics

The author presents his experience in teaching at a graduate level the quantal exposition of a new non-statistically based paradigm of physics and thermodynamics. This paradigm, called the Unified Quantum Theory of Mechanics and Thermodynamics, applies to all systems large or small (including one particle systems) either in a state of thermodynamic (i.e. stable) equilibrium or not in a state of thermodynamic equilibrium. It uses as its primitives inertial mass, force, and time and introduces the laws of thermodynamics in the most unambiguous and general formulations found in the literature. Starting with a precise definition of system and of state followed by statements and corollaries of the laws of thermodynamics, the thermodynamic formalism is developed without circularity and ambiguity. In this quantal exposition of the new paradigm, a brief review of the formalism of thermodynamics as a general science not limited to stable equilibrium and large (macroscopic) systems as well as a very brief summary of the three prevalent formalisms in classical physics are presented followed by a presentation and development of solutions for a number of elementary problems in quantum physics (e.g., a particle in a box, a harmonic oscillator, a rigid rotor, etc.). These solutions and the maximum entropy principle are then used in a constrained optimization to develop the canonical and grand canonical distributions for Fermi-Dirac and Bose-Einstein types of particles, i.e. for fermions and bosons. This is done without the use of analogies between statistical and thermodynamic results and without additional hypotheses such as the ergodic hypothesis of statistical mechanics. These distributions are then employed under various assumptions (i.e. the Boltzmann, constant-potential, point-particle, and continuous eigenvalue-spectrum approximations) to derive the corresponding thermodynamic property expressions for perfect, semi-perfect (ideal), and Sommerfeld gases as well as for mixtures of ionized and dissociated gases. In a similar fashion but with a change from a single- to a multi-particle partition function and with the addition of various inter-particle potentials for two-particle interactions (e.g., the Lennard-Jones potential, the square-well potential, etc.), expressions for the thermodynamic properties of dense gases are developed and presented. An initial version of this paper was published in July of 2006 in the proceedings of ECOS’06, Aghia Pelagia, Crete, Greece.

Semiclassical states in loop quantum gravity: an introduction

Unifying general relativity and quantum mechanics is a great challenge left to us by Einstein. To face this challenge, considerable progress has been made in non-perturbative canonical (loop) quantum gravity during the past 20 years. The kinematical Hilbert space of the quantum theory is constructed rigorously. However, the semiclassical analysis of the theory is still a crucial and open issue. In this review, we first introduce our work on constructing a semiclassical weave state, using the \(\hat Q\)[ω] operator on the kinematical Hilbert space of loop quantum gravity. Then we give an introduction to the two different approaches currently investigated for constructing coherent states in the kinematical Hilbert space. The current status of semiclassical analysis in loop quantum gravity is then summarized.

Quantum motion in complex space

Abstract This paper is dedicated to the development of a general theory unifying classical and quantum mechanics in complex space, and to the conveyance of the philosophy that what have been considered as probabilistic quantum events have a common origin from the particle’s deterministic motion in complex space. We postulate that the actual scenario of dynamic motion happens in complex space and what we customarily consider as physical reality is merely the projection of the actual scenario into the real space. The proposed theory employs complex-extended classical mechanics to describe and model quantum systems in such a way that all the particle-like properties can be reserved due to its classical nature and in the meanwhile, all the wave-like properties are manifested naturally via the multi-path behavior of complex trajectories. The proposed framework of complex mechanics makes use of classical concepts and tools to deal with particle’s quantum behavior by the introduction of a complex Hamiltonian from which complex Hamilton equations describing particle’s quantum motion are derived in a form of Newton’s second law defined in complex space. Complex mechanics is then connected with quantum mechanics by showing the equivalence between the complex Hamilton–Jacobi equation and Schrodinger equation. The solutions of the complex Hamilton equations give us the complex trajectories traced by a particle, which are found to be non-unique. It is this non-uniqueness of the complex trajectories projected into real space that produces the multi-path phenomenon and the observed wave behavior of a material particle in the real space. This conclusion seems to be consistent with that of Elnaschie e (∞) space–time [Elnaschie MS. The Feynman path intergal and E -infinity from the two-slit Geclanken experiment. Int J Nonlinear Sci Numer Simul 2005;6(4):335–42; Elnaschie MS. A review of the E -infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals 2004;19:209–36; Elnaschie MS. Elementry number theory in superstrings, loop quantum mechanics, twisters and E -infinity high energy physics. Chaos, Solitons & Fractals 2006;27:297–330].