Motion in bimetric type theories of gravity

The problem of motion of different test particles, charged and spinning objects with a constant spin tensor in different versions of the bimetric theory of gravity is considered by deriving their corresponding path and path deviation equations using a modified Bazanski Lagrangian. Such a Lagrangian, as in the framework of Riemannian geometry, has a capability to obtain path and path deviations of any object simultaneously. This method enables us to derive the path and path deviation equations of different objects orbiting in very strong gravitational fields.     

Slice energy in higher-order gravity theories and conformal transformations

We study the generic transport of slice energy between the scalar field generated by the conformal transformation of higher-order gravity theories and the matter component. We give precise relations for this exchange in the cases of dust and perfect fluids. We show that, unless we are in a stationary spacetime where slice energy is always conserved, in non-stationary situations, contributions to the total slice energy depend on whether or not test matter follows geodesics in both frame representations of the dynamics, that is, on whether or not the two conformally related frames are physically indistinguishable.     

The use of symbolic calculations in post-Riemannian and multidimensional theories of gravity

We have developed new methods of using symbolic computer calculations for four- and higher-dimensional, geometrically generalized spaces. In particular, we work with differential identities in order to check the variational field equations of a conformal theory of gravity with a scalar field in Weyl-Cartan space. To simplify the navigation, we have worked out a graphic user interface, making it possible to solve problems of a post-Riemannian theory of gravity in Weyl-Cartan space, as well as those of the Kaluza-Klein five-dimensional unified theory of gravity and electromagnetism, in particular, in the external form formalism.     

Dilaton-scalar models in the context of generalized affine gravity theories: Their properties and integrability

Nowadays it is widely accepted that the evolution of the Universe was driven by some scalar degrees of freedom both on its early stage and at present. The corresponding cosmological models often involve some scalar fields introduced ad hoc. In this paper we cultivate a different approach, based on a derivation of new scalar degrees of freedom from fundamental modifications of Einstein’s gravity. In elaboration of our previous work, we here investigate the properties of dilaton-scalar gravity obtained by dimensional reductions of a recently proposed affine generalized gravity theory. We show that these models possess the same symmetries as the related models of GR with ordinary scalar fields. As a result, for rather a general class of dilaton-scalar gravity models, we construct additional first integrals and formulate an integral equation well suited for solving by iterations.     

On black hole radiation spectrum in loop quantum gravity

We propose an alternative analysis of black hole entropy from loop quantum gravity (LQG) to reconcile Hawking’s semiclassical results with the statistical mechanics treatment of LQG for all values of the Barbero-Immirzi (BI) parameter. In particular, using the average area of the punctures, we have calculated the corresponding entropy, identified the BI parameter and derived the radiation spectrum in terms of the possible punctures.     

First passage time of discretized plates with geometrical nonlinearity

The first passage time of discretized plate structures subjected to transversal and in-plane intensive transient loadings treated as nonstationary random processes is studied. The mean rate of various crossings for the nonstationary random response is evaluated using the definitions of Vanmarcke and Roberts. The definition of Roberts is extended to include clump size and clustering effects in similar spirit to that of Vanmarcke. Approximated first passage probabilities based on these definitions of mean rate of various crossings are obtained for some square steel plate structures whose response statistics are derived by an approach employing the Ito's calculus.     

Discrete time adaptive control of linear systems with preload nonlinearity

In this note a method is presented for doing discrete time adaptive control of a nonlinear system which is given by a cascade connection of a preload nonlinearity followed by a linear system. It is shown that the algorithm will ensure that the closed loop system is globally convergent with a specific residue and stable for both the deterministic and stochastic cases.     

Theoretical comparison of quantum Zeno gates and logic gates based on the cross-Kerr nonlinearity

Quantum logic operations can be implemented using nonlinear phase shifts (the Kerr effect) or the quantum Zeno effect based on strong two-photon absorption. Both approaches utilize three-level atoms, where the upper level is tuned on resonance for the Zeno gates and off-resonance for the nonlinear phase gates. The performance of nonlinear phase gates and Zeno gates are compared under conditions where the parameters of the resonant cavities and three-level atoms are the same in both cases. It is found that the expected performance is comparable for the two approaches despite the fundamental differences between the Zeno and Kerr effects.     

Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity

This paper is concerned with the problem of robust exponential stability for a class of hybrid stochastic neural networks with mixed time-delays and Markovian jumping parameters. In this paper, free-weighting matrices are employed to express the relationship between the terms in the Leibniz–Newton formula. Based on the relationship, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions for the mixed time-delays neural networks with Markovian jumping parameters. Finally, two simulation examples are provided to demonstrate the effectiveness of the results developed.     

Hitting time of quantum walks with perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy’s work and the perturbation bounds with Weyl’s perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is bounded from above by the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.     

Analysis of optical parity gates of generating Bell state for quantum information and secure quantum communication via weak cross-Kerr nonlinearity under decoherence effect

We demonstrate the advantages of an optical parity gate using weak cross-Kerr nonlinearities (XKNLs), quantum bus (qubus) beams, and photon number resolving (PNR) measurement through our analysis, utilizing a master equation under the decoherence effect (occurred the dephasing and photon loss). To generate Bell states, parity gates based on quantum non-demolition measurement using XKNL are extensively employed in quantum information processing. When designing a parity gate via XKNL, the parity gate can be diversely constructed according to the measurement strategies. In practice, the interactions of XKNLs in optical fiber are inevitable under the decoherence effect. Thus, by our analysis of the decoherence effect, we show that the designed parity gate employing homodyne measurement would not be expected to provide reliable quantum operation. Furthermore, compared with a parity gate using a displacement operator and PNR measurement, we conclude there is experimental benefit from implementation of a parity gate via qubus beams and PNR measurement under the decoherence effect.     

MFD models and time delays; some consequences for identification

A general relationship is established between the coefficients of a general MFD model and its associated Markov parameters. This result is used to derive necessary and sufficient conditions for the appearance of time delays in general MFD models. These conditions involve dependencies between some coefficients of the MFD models. Finally, it is indicated how these dependencies can possibly be incorporated in equation-error identification techniques retaining the favourable property of linearity in the parameters.     

开放量子行走的击中时分析

作为量子搜索算法研究的一个基本工具,量子行走是一个重要研究课题。同时,击中时是衡量量子行走到达某一目标顶点速度的标准,对量子算法研究具有广泛的应用。在开放量子环境下,给出开放量子行走的四种击中时定义：单次击中时、并行击中时、平均击中时和极限击中时。区分四种击中时,说明前两种用于刻画开放量子行走局部到达目标顶点,而后两种从全局和极限角度分析目标顶点到达情况。针对同质开放量子行走、异质开放量子行走和嵌套开放量子行走,分别给出四种击中时具体计算。     

Discrete quantum Fourier transform using weak cross-Kerr nonlinearity and displacement operator and photon-number-resolving measurement under the decoherence effect

We present a scheme for implementing discrete quantum Fourier transform (DQFT) with robustness against the decoherence effect using weak cross-Kerr nonlinearities (XKNLs). The multi-photon DQFT scheme can be achieved by operating the controlled path and merging path gates that are formed with weak XKNLs and linear optical devices. To enhance feasibility under the decoherence effect, in practice, we utilize a displacement operator and photon-number-resolving measurement in the optical gate using XKNLs. Consequently, when there is a strong amplitude of the coherent state, we demonstrate that it is possible to experimentally implement the DQFT scheme, utilizing current technology, with a certain probability of success under the decoherence effect.     

Discrete time adaptive control of linear dynamic systems with a two-segment piecewise-linear asymmetric nonlinearity

In this note a method is presented for doing discrete adaptive control of a nonlinear system which is given by a cascade connection of a "two-segment piecewise-linear asymmetric nonlinearity" followed by a linear system. A switching gain sequence is introduced to make the parameter identification time invariant. The algorithm will ensure that the closed-loop system is globally convergent and stable for both the deterministic and stochastic cases.     

Quantum state tomography from observable time traces in closed quantum systems

The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time traces to identify the initial quantum state of a closed quantum system, based on the state space approach in the control theory. In the informationally complete scenario, we show that with a linear regression estimation (LRE), the mean squared error (MSE) scales as O (1/N), where N is the resource number. In the informationally incomplete scenario, we introduce regularization LRE to perform the state tomography task. We employ PBH test to demonstrate that closed quantum systems with only one observable are informationally incomplete and propose using d ? 1 observables, where d is the dimension of the quantum state, for informational completeness. Numerical examples demonstrate the effectiveness of our method.     

Propagator approach for time evolving wave packets in the quantum kicked rotator

We outline a method for time evolving narrow wave packets in the quantum-mechanical kicked rotator, an archetype of quantum chaos. We employ the approximation that the boundary conditions may be neglected. The evolution between kicks may then be carried out using the one-dimensional free-particle propagator.     

Improved DNA-sticker arithmetic: tube-encoded-carry, Logarithmic Number System and Monte-Carlo methods

The sticker model of computation, implemented using robotic processing of DNA, manipulates in parallel many bitstrings, called strands, that are contained in a limited number of tubes. Prior sticker arithmetic algorithms, patterned on digital-electronics, generate carry bits in the strand, either wasting bits or using a clear operation (with problematic biochemical implementation). The novel addition algorithm here does not need to record the carry. Instead, which tube holds a particular strand implicitly encodes the carry. The speed and number of tubes are half that of prior approaches. Further encoding data in the Logarithmic Number System (LNS) allows such integer operations to perform cost-effective real multiplications, divisions and roots. An example LNS Euclidian norm is more efficient than prior methods, assuming perfect operations. Unfortunately, DNA-stickers are unreliable. This paper uses sticker unreliability as a source of randomness to implement Monte-Carlo (MC) arithmetic (previously fabricated in silicon at the cost of pseudo-random generators). With stickers, the randomness is free. MC engineering mimics natural systems using unreliable but redundant components. Here, MC randomness is only useful in low-order bits. Multiple re-testing of the same bit (“refinement”) trades improved reliability for slower operation using more tubes. Simulations (with different sizes, probabilities and refinement) show that increasing refinement as a function of bit position allows imperfect implementations to achieve suitable MC strand-error distributions, predicting 1000x speed-mass advantage of sticker-MCLNS over conventional supercomputers.     

One-mode quantum Gaussian channels: Structure and quantum capacity

A complete classification of one-mode Gaussian channels is given up to canonical unitary equivalence. We also comment on the quantum capacity of these channels. A channel complementary to the quantum channel with additive classical Gaussian noise is described, providing an example of a one-mode Gaussian channel which is neither degradable nor antidegradable.