Searcharxiv⌕ Search

arXiv subjects

J. Novotny

Publications and source records attributed to J. Novotny.

At least 19 recordsLinked to original sources
arXiv2023

Two-particle Hadamard walk on dynamically percolated line and circle

Asymptotic dynamics of a Hadamard walk of two non-interacting quantum particles on a dynamically percolated finite line or a circle is investigated. We construct a basis of the attractor space of the corresponding random-unitary dynamics and prove the completeness of our solution. In comparison to the one-particle case, the structure of the attractor space is much more complex, resulting in intriguing asymptotic dynamics. General results are illustrated on two examples. First, for circles of length not divisible by 4 the boundary conditions reduces the number of attractors considerably, allowing for fully analytic solution. Second, we investigate line of length 4 and determine the asymptotic cycle of reduced coin states and position distributions, focusing on the correlations between the two particles. Our results show that a random unitary evolution, which is a combination of quantum dynamics and a classical stochasticity, leads to correlations between initially uncorrelated particles. This is not possible for purely unitary evolution of non-interacting quantum particles. The shared dynamically percolated graph can thus be considered as a weak form of interaction.

quant-ph↗
arXiv2021

Magnetoresistive Sensor Detectivity: A Comparative Analysis

We report on the noise performance characteristics of magnetic sensors using both magnetic tunnel junction (MTJ) and giant magnetoresistance (GMR) elements. Each sensor studied has a notably different noise and detectivity. Of the sensors we measured, those based on GMR multilayers have the lowest noise and detectivity. However, the GMR sensor also has a significantly smaller linear range. To make a direct comparison between sensors we scale the linear operating ranges of each sensor to be the same. This is the phenomenological equivalent of modifying the flux concentration. Upon scaling the low frequency detectivity of the TMR sensors becomes essentially equal to that of the GMR sensor. Using the scaling approach we are able to place the detectivity in the context of other key parameters, namely size and power consumption. Lastly, we use this technique to examine the upper limit for magnetoresistive sensor performance based on a notional MTJ sensor using present record setting TMR values.

cond-mat.mtrl-sci↗
arXiv2016

New Superpotential in Conservation Laws in General Relativity

This work refers to the new formula for the superpotential Uikl in conservation laws in general relativity satisfying the integral and differential conservation laws within the Schwarzschild metric. The new superpotential is composed of two terms. The first term is based on Mollers concept and its a function of the metric gik and its first derivative only. The second term is the antisymmetric tensor density of weight plus one and it consists of higher derivatives of the metric gik. Although the new superpotential consists of higher derivatives of the metric gik it might bring a new evaluation of the conservative quantities in general relativity

gr-qc↗
arXiv2011

Pi-eta scattering and the resummation of vacuum fluctuation in three-flavour ChPT

We discuss various aspects of resummed chiral perturbation theory, which was developed recently in order to consistently include the possibility of large vacuum fluctuations of the ss-pairs and the scenario with smaller value of the chiral condensate for N_f=3. The subtleties of this approach are illustrated using a concrete example of observables connected with pi-eta scattering. This process seems to be a suitable theoretical laboratory for this purpose due to its sensitivity to the values of the O(p^4) LEC's, namely to the values of the fluctuation parameters L4 and L6. We discuss several issues in detail, namely the choice of `good' observables and properties of their bare expansions, the `safe' reparametrization in terms of physical observables, the implementation of exact perturbative unitarity and exact renormalization scale independence, the role of higher order remainders and their estimates. We make a detailed comparison with standard chiral perturbation theory and use generalized ChPT as well as resonance chiral theory to estimate the higher order remainders.

hep-ph↗
arXiv2009

Construction of the eta->3pi (and K->3pi) amplitudes using dispersive approach

The dispersive approach based only on very general principles, unitarity, analyticity and crossing symmetry, combined with chiral counting enables to construct fully relativistic model-independent representations of the eta and K three-pion decays valid up to and including two-loop corrections. Here we demonstrate the procedure on the eta->3pi^0 decay. We perform possible matchings of our dispersive approach with the two-loop ChPT result and briefly discuss corresponding predictions of the Dalitz plot slope parameter alpha.

hep-ph↗
arXiv2009

Asymptotic Evolution of Random Unitary Operations

We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.

quant-ph↗
arXiv2009

Dispersive construction of two-loop P->3π(P=K,η) amplitudes

The branching ratio of the η->3πdecay is an important source of information on the value of the quark mass ratio 1/R=(m_d-m_u)/(m_s-\hat m). Furthermore, isospin breaking effects in the decays K->3πprovide information on the pion scattering lengths. The cusp effect in the K->3πdecays is presently being analyzed by the NA48 and KTeV experiments. From the theoretical point of view, these processes have been studied by different methods. We propose a unified and relativistic treatment relying on very general principles, unitarity, analyticity and crossing symmetry, combined with chiral counting, in order to construct model-independent representations of the corresponding amplitudes that are valid at two loops. A general description of the procedure is given and is illustrated in the case of the ηdecay amplitude in the leading order in the isospin breaking.

hep-ph↗
arXiv2009

Random unitary dynamics of quantum networks

We investigate the asymptotic dynamics of quantum networks under repeated applications of random unitary operations. It is shown that in the asymptotic limit of large numbers of iterations this dynamics is generally governed by a typically low dimensional attractor space. This space is determined completely by the unitary operations involved and it is independent of the probabilities with which these unitary operations are applied. Based on this general feature analytical results are presented for the asymptotic dynamics of arbitrarily large cyclic qubit networks whose nodes are coupled by randomly applied controlled-NOT operations.

quant-ph↗
arXiv2008

Dispersive Approach to Chiral Perturbation Theory

We generalise the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the (2 -> 2) scattering of all the pseudoscalar octet mesons (pi, K, eta). We formulate it in a general way and include also a discussion of the assumptions of the theorem. It is used to obtain the amplitudes of all such processes in the isospin limit to the one-loop order (and can be straightforwardly extended to two loops) independently on the particular power-counting scheme of the chiral perturbation theory in question. The results in this general form are presented.

hep-ph↗
arXiv2008

The eta decay constant in `resummed' chiral perturbation theory

The recently developed 'Resummed' ChPT is illustrated on the case of pseudoscalar meson decay constants. We try to get an estimate of the eta decay constant, which is not well known from experiments, while using several ways including the Generalized ChPT Lagrangian to gather information beyond Standard next-to-leading order. We compare the results to published ChPT predictions, our own Standard ChPT calculations and available phenomenological estimates.

hep-ph↗
arXiv2007

Network implementation of covariant two-qubit quantum operations

A six-qubit quantum network consisting of conditional unitary gates is presented which is capable of implementing a large class of covariant two-qubit quantum operations. Optimal covariant NOT operations for one and two-qubit systems are special cases contained in this class. The design of this quantum network exploits basic algebraic properties which also shed new light onto these covariant quantum processes.

quant-ph↗
arXiv2006

Completely positive covariant two-qubit quantum processes and optimal quantum NOT operations for entangled qubit pairs

The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly.

quant-ph↗
arXiv2004

Optimal copying of entangled two-qubit states

We investigate the problem of copying pure two-qubit states of a given degree of entanglement in an optimal way. Completely positive covariant quantum operations are constructed which maximize the fidelity of the output states with respect to two separable copies. These optimal copying processes hint at the intricate relationship between fundamental laws of quantum theory and entanglement.

quant-ph↗
arXiv2004

The eta->pi^0 pi^0 gamma gamma decay in GCHPT

Calculations of eta->pi^0 pi^0 gamma gamma decay in Generalized chiral perturbation theory are presented. Tree level and next-to-leading corrections are involved. Sensitivity to the violation of the standard counting is discussed.

hep-ph↗
arXiv2003

pi-eta scattering in generalized chiral perturbation theory

We calculate the amplitude of pi-eta scattering in generalized chiral perturbation theory at the order O(p^4) and present preliminary results of the numerical analysis of the S-wave scattering length, which seems to be particularly sensitive to the deviations from the standard case.

hep-ph↗
arXiv2002

Some aspects of Dalitz decay pi0 -> e+ e- gamma

A calculation of the Dalitz decay in next-to-leading order in chiral perturbation theory of two flavour case extended by virtual photons is presented. The whole kinematic sector is covered and realistic experimental situation is discussed.

hep-ph↗
arXiv2002

Einstein-Maxwell fields generated from the gamma-metric and their limits

Two solutions of the coupled Einstein-Maxwell field equations are found by means of the Horsky-Mitskievitch generating conjecture. The vacuum limit of those obtained classes of spacetimes is the seed gamma-metric and each of the generated solutions is connected with one Killing vector of the seed spacetime. Some of the limiting cases of our solutions are identified with already known metrics, the relations among various limits are illustrated through a limiting diagram. We also verify our calculation through the Ernst potentials. The existence of circular geodesics is briefly discussed in the Appendix.

gr-qc↗