Quantum Domain Research Articles

Truth as Contextual Correspondence in Quantum Mechanics

The semantics underlying the propositional structure of Hilbert space quantum mechanics involves an inherent ambiguity concerning the impossibility of assigning definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. Although the preceding Kochen-Specker result forbids a global, absolute assignment of truth values to quantum mechanical propositions, it does not exclude ones that are contextual. In this respect, the Bub-Clifton “uniqueness theorem” is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a suitable “preferred” observable. It is suggested that the most natural choice of the latter, especially for confronting the problem of truth valuation in quantum mechanics, results in the determinateness of the observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The resulting account of truth is compatible with a realist conception of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature.

Statistical aspects of harmonic oscillator under minimal length supposition

This paper attempts to study the influence of the Generalized Uncertainty Principle (GUP) on the statistical aspects of the N-one dimensional harmonic oscillator. The Investigations are introduced in both classical and quantum domains. It is shown how the GUP scenario modifies the N-oscillator canonical partition functions of each of the approaches. The modifications of the thermodynamical parameters such as the mean energy and entropy are obtained. The applied method stands on the perturbation technique and is simple and the modified characteristics are applicable and do not have the complexity of the other parallel approaches. The deformation parameter of considered GUP model, also estimated for an ensemble of hydrogen atoms.

Quantum measurements and Landauer’s principle

Information processing systems must obey laws of physics. One of particular examples of this general statement is known as Landauer’s principle - irreversible operations (such as erasure) performed by any computing device at finite temperature have to dissipate some amount of heat bound from below. Together with other results of this kind, Landauer’s principle represents a fundamental limit any modern or future computer must obey.We discuss interpretation of the physics behind the Landauer’s principle using a model of Unruh-DeWitt detector. Of particular interest is the validity of this limit in quantum domain. We systematically study finite time effects. It is shown, in particular, that in high temperature limit finiteness of measurement time leads to renormalization of the detector’s temperature.

Orbital free DFT versus single density equation: a perspective through quantum domain behavior of a classically chaotic system.

The orbital free density functional theory and the single density equation approach are formally equivalent. An orbital free density based quantum dynamical strategy is used to study the quantum-classical correspondence in both weakly and strongly coupled van der Pol and Duffing oscillators in the presence of an external electric field in one dimension. The resulting quantum hydrodynamic equations of motion are solved through an implicit Euler type real space method involving a moving weighted least square technique. The Lagrangian framework used here allows the numerical grid points to follow the wave packet trajectory. The associated classical equations of motion are solved using a sixth order Runge-Kutta method and the Ehrenfest dynamics is followed through the solution of the time dependent Schrodinger equation using a time dependent Fourier Grid Hamiltonian technique. Various diagnostics reveal a close parallelism between classical regular as well as chaotic dynamics and that obtained from the Bohmian mechanics.

Quantum Domains for Macroscopic Transport Effects in Nanostructures with Control Topology: Optics and e-Conductivity

The nanostructures with different morphology have been obtained by us by methods of both direct laser modification (from cw to fs laser radiation) of the target surface/thin films and laser evaporation of the target substance in liquid to produce the colloid systems, and then – to deposite substance on substrate from colloid, and also – by a single drop deposition technique. The analysis of induced nanostructures has been carried out by absorption spectroscopy, scanning electron microscopy and transmission electron microscopy. The island conductivity is dominant for the nanocluster semiconductor systems induced by laser ablation technique, and electroresistance can dramatically decrease due to spontaneous selected multichannel/parallel electron transportation trajectories. A tunneling quantum coherent effect takes place for electron conductivity for the case.

The Casimir force between an ideal metal plate and a dissipative dielectric slab

In this research, a general formula for the Casimir force between ideal metal plate and a dissipative dielectric slab has been obtained. The dielectric function of the slab is assumed to be an arbitrary complex function of frequency satisfying Kramers–Kronig relations. A classical expression for the radiation pressure of the vacuum fields on the slab is presented by using the Maxwell stress tensor. With the transition to the quantum domain and using the fluctuation dissipation theorem and Kubo's formula, the resulting expression is written in terms of the imaginary part of the vector potential Green functions components of the system. Finally, by computing the Green function, the Casimir force on the slab is obtained. This formalism enables us to calculate the Casimir force without resorting to the explicit form of the field operators. The general expression is confirmed by limiting and comparing with one of the previous works.

Energetics and kinetics of vacancies in monolayer graphene boron nitride heterostructures

Graphene and boron nitride (GPBN) heterostructures provide a viable way to realize tunable bandgap, promising new opportunities in graphene-based nanoelectronic and optoelectronic devices. In the present study, we investigated the interplay between vacancies and graphene/h-BN interfaces in monolayer GPBN heterostructures. The energetics and kinetics of monovacancies and divacancies in monolayer GPBN heterostructures were examined using first-principle calculations. The interfaces were shown to be preferential locations for vacancy segregation. Meanwhile the kinetics of vacancies was found to be noticeably modified at interfaces, evidenced by the minimum energy paths and associated migration barriers calculations. The role of interfacial bonding configurations, energy states and polarization on the formation and diffusion of vacancies were discussed. Additionally we demonstrated that it is important to recognize the dissimilarities in the diffusion prefactor for different vacancies for accurate determination of the vacancy diffusion coefficient. Our results provide essential data for the modeling of vacancies in GPBN heterostructures, and important insights towards the precise engineering of defects, interfaces and quantum domains in the design of GPBN-based devices.

Quantum and classical separability of spin-orbit laser modes

In this work we investigate the quantum noise properties of polarization vortices in connection with an intensity based Clauser-Horne-Shimony-Holt inequality for their spin-orbit separability. We evaluate the inequality for different input quantum states and the corresponding intensity fluctuations. The roles played by coherence and photon number squeezing provide a suitable framework for characterizing pure state spin-orbit entanglement. Structural inseparability of the spin-orbit mode requires coherence, an issue concerning either classical or quantum descriptions. In both cases, it can be witnessed by violation of this intensity based CHSH inequality. However, in the quantum domain, entanglement requires both coherence and reduced photon number fluctuations.

Quantum correlations expressed as information and entropic inequalities for composite and noncomposite systems

For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for von Neumann entropies of quantum states determined by the density operators. We extend the relations of Shannon and Tsallis entropies to the entropies of conditional probability distributions known for composite systems to the case of noncomposite systems. We give a review of the approach to construct the tomographic-probability distributions for qudit systems and present the entropic and information inequalities for spin tomograms, as well as the subadditivity and strong subadditivity conditions for tomograms of the both noncomposite and composite system states.

Towards a Quantum Domain Theory: Order-enrichment and Fixpoints in W*-algebras

We discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science. From a computer scientist point of view, we explain some fundamental results of operator theory and their relevance in the context of domain theory. In particular, we consider the category W* of W*-algebras together with normal sub-unital maps, provide an order-enrichment for this category and exhibit a class of its endofunctors with a canonical fixpoint.

Action, quantum computation and the structure of the Yang–Mills Lagrangian

We seek to interpret the notions of action and Lagrangian in the quantum domain in terms of a quantum computational paradigm. This effort was inspired by work of Toffoli in the classical case. We claim that in this paradigm an action integral may itself be regarded as a quantum “macroprogram” with the generating Lagrangian density playing the role of a quantum “microprogram” describing an underlying quantum process, in rough analogy with the way a \(\lambda \)-expression (in simply typed \(\lambda \)-calculus) may be unfolded to reveal an underlying natural deduction. We carry out such an unfolding for the Yang–Mills Lagrangian (including a gauge fixing term) to reveal a simple underlying quantum microprogram which in this case effects the variation of a fermion tuple consequent upon a quantized, generically deformed, gauge rotation of the tuple.

Beables/Observables in Classical and Quantum Gravity

Observables 'are observed' whereas beables just 'are'. This gives beables more scope in the cosmological and quantum domains. Both observables and beables are entities that form 'brackets' with 'the constraints' that are 'equal to' zero. We explain how depending on circumstances, these could be, e.g., Poisson, Dirac, commutator, histories, Schouten-Nijenhuis, double or Nambu brackets, first-class, gauge, linear or effective constraints, and strong, weak or weak-effective equalities. The Dirac-Bergmann distinction in notions of gauge leads to further notions of observables or beables, and is tied to a number of diffeomorphism-specific subtleties. Thus we cover a wide range of notions of observables or beables that occur in classical and quantum gravitational theories: Dirac, Kucha\v{r}, effective, Bergmann, histories, multisymplectic, master, Nambu and bi-. Indeed this review covers a representatively wide range of such theories: general relativity, loop quantum gravity, histories theory, supergravity and M-theory.

A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.

Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a “hairline” solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.

Accurate Energy Spectrum for the Quantum Yang-Mills Mechanics with Nonlinear Color Oscillations

Yang-Mills theory as the foundation for quantum chromodynamics is a non-Abelian gauge theory with self-interactions between vector particles. Here, we study the Yang-Mills Hamiltonian with nonlinear color oscillations in the absence of external sources corresponding to the group $SU(2)$. In the quantum domain, we diagonalize the Hamiltonian using the optimized trigonometric basis expansion method and find accurate energy eigenvalues and eigenfunctions for one and two degrees of freedom. We also compare our results with the semiclassical solutions.

Manifesting the Quantum World

In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the process by which what Sellars called the Manifest Image of the world comes into being. This process consists in the progressive differentiation of an intrinsically undifferentiated entity. By entering into reflexive spatial relations, this gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified. If there is a distinctly quantum domain, it is a non-spatial and non-temporal dimension across which the transition from the unity of this entity to the multiplicity of the world takes place. Instead of being constituents of the physical world, subatomic particles, atoms, and molecules are instrumental in its manifestation. These conclusions are based on the following interpretive principle: whenever calculating probabilities calls for the addition of amplitudes, the distinctions we make between the alternatives lack objective reality. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete: the existence of a real-valued spatiotemporal background is an unrealistic idealization. This guarantees the existence of observables whose values are real *per se*, as against "real by virtue of being indicated by the values of observables that are real *per se*." Applied to alternatives involving distinctions between things, it implies that, intrinsically, all fundamental particles are numerically identical and thus identifiable with the aforementioned undifferentiated entity.

On the relation between quantum mechanical and neo-mechanistic ontologies and explanatory strategies

Advocates of the New Mechanicism in philosophy of science argue that scientific explanation often consists in describing mechanisms responsible for natural phenomena. Despite its successes, one might think that this approach does not square with the ontological strictures of quantum mechanics. New Mechanists suppose that mechanisms are composed of objects with definite properties, which are interconnected via local causal interactions. Quantum mechanics calls these suppositions into question. Since mechanisms are hierarchical it appears that even macroscopic mechanisms must supervene on a set of “objects” that behave non-classically. In this paper we argue, in part by appeal to the theory of quantum decoherence, that the universal validity of quantum mechanics does not undermine neo-mechanistic ontological and explanatory claims as they occur within in classical domains. Additionally, we argue that by relaxation of certain classical assumptions, mechanistic explanatory strategies can sometimes be carried over into the quantum domain.

A Carleman estimate for infinite cylindrical quantum domains and the application to inverse problems

We consider the inverse problem of determining the time-independent scalar potential q of the dynamic Schrödinger equation in an infinite cylindrical domain Ω, from one Neumann boundary observation of the solution. Assuming that q is known outside some fixed compact subset of Ω, we prove that q may be Lipschitz stably retrieved by choosing the Dirichlet boundary condition of the system suitably. Since the proof is by means of a global Carleman estimate designed specifically for the Schrödinger operator acting in an unbounded cylindrical domain, the measurement of the Neumann data is performed on an infinitely extended subboundary of the cylinder.

Quantum Limits on the Energy Consumption of Optical Transmission Systems

The search for schemes that minimize the energy associated with the transmission of information is a longstanding fundamental issue in communication theory. In this paper we extend fundamental limits to the energy consumption per unit of information, as given by Shannon's theory, to the quantum domain. Unlike previous studies, we address a scenario where the signal may be manipulated in an arbitrary way while propagating from the transmitter to the receiver. This situation characterizes many realistic scenarios, such as multi-span fiber-optic communication systems. We obtain the ultimate quantum limit on the energy consumption in this scenario and propose a simple binary energy modulation scheme that approaches this limit within one order of magnitude for practically relevant values of spectral efficiency. Under the same conditions, the quantum energy consumption limit of the standard optically amplified coherent communication scheme is three orders of magnitude above the ultimate identified limit. Throughout the paper we consider transmission of classical information over a quantum channel.

Photocreation of a quantum domain and its detection by inelastic X-ray scattering and X-ray CARS

We briefly argue the concept of a quantum domain and propose its detection using X-ray inelastic scattering and X-ray coherent anti-Stokes Raman scattering (CARS). The quantum domain is defined as a spatial region of which the phase state is converted to a different one from that in the background. In a case where photoinduced phase transitions are allowed to exhibit, such a domain has a relatively low excitation energy and is expected to be detected experimentally. Especially the X-ray inelastic scattering and the CARS are attractive methods, since they can give information of both the momentum and the energy.