arXiv subjects

M. Martinis

Publications and source records attributed to M. Martinis.

18 recordsLinked to original sources

arXiv2010

On the Gravitational Energy Shift for matter waves

The gravitational energy shift for photons is extended to all mass-equivalent energies $E = mc^2$, obeying the quantum condition $E = hν$.On an example of a relativistic binary system, it was shown that the gravitational energy shift would imply,in contrast to Newtonian gravity, the gravitational attraction between full mass-equivalent energies. The corresponding space-time metric becomes exponential. A good agreement was found with all results of weak field tests of General relativity. The strong field effects in a binary system can be easily studied. A long standing problems of Pioneer and other flyby anomalies were also discussed in connection with the violation of total energy conservation. It was shown that relatively small energy non-conservation during the change of the orbit type could explain these persistent anomalies.

gr-qc↗

arXiv2007

K-minus Estimator Approach to Large Scale Structure

Self similar 3D distributions of point-particles, with a given quasifractal dimension D, were generated on a Menger sponge model and then compared with \textit{2dfGRS} and \textit{Virgo project} data \footnote{http://www.mso.anu.edu.au/2dFGRS/, http://www.mpa-garching.mpg.de/Virgo/}. Using the principle of local knowledge, it is argued that in a finite volume of space only the two-point minus estimator is acceptable in the correlation analysis of self similar spatial distributions. In this sense, we have simplified the Pietronero-Labini correlative analysis by defining a K-minus estimator, which when applied to 2dfGRS data revealed the quasifractal dimension $D\approx 2$ as expected. In our approach the K-minus estimator is used only locally. Dimensions between D = 1 and D = 1.7, as suggested by the standard $ξ(r)$ analysis, were found to be fallacy of the method. In order to visualize spatial quasifractal objects, we created a small software program called \textit{RoPo} (''Rotate Points''). This program illustrates and manifests local correlative analysis in which the visual inspection emerged as a first step and a key part of the method. Finally, we discuss importance and perspective of the visual inspection on available real and simulated distributions. It is also argued that results of contemporary cosmological simulations do not faithfully represent real data, as they show a formation of ever increasing collapsars. We consent that 2dfGRS data are reminiscent of some kind of underlying turbulence like effects in action.

astro-ph↗

arXiv2005

Existence of Time Operator for a Singular Harmonic Oscillator

The time operator for a quantum singular oscillator of the Calogero-Sutherland type is constructed in terms of the generators of the SU(1,1) group. In the space spanned by the eigenstates of the Hamiltonian, the time operator is not self-adjoint. We show, that the time-energy uncertainty relation can be given the meaning within the Barut-Girardello coherent states defined for the singular oscillator.We have also shown the relationship with the time-of-arrival operator of Aharonov and Bohm.

quant-ph↗

arXiv2005

Space-Time Non-Commutativity near Horizon of a Black Hole

We consider dynamics of a quantum scalar field, minimally coupled to classical gravity, in the near-horizon region of a Schwarzschild black-hole. It is described by a static Klein-Gordon operator which in the near-horizon region reduces to a scale invariant Hamiltonian of the system. This Hamiltonian is not essentially self-adjoint, but it admits a one-parameter family of self-adjoint extension. The time-energy uncertainty relation, which can be related to the thermal black-hole mass fluctuations, requires explicit construction of a time operator near-horizon. We present its derivation in terms of generators of the affine group. Matrix elements involving the time operator should be evaluated in the affine coherent state representation.

gr-qc↗

arXiv2003

Time operator for a quantum many-body system with SU(1,1) dynamical symmetry

The time operator canonically conjugated to the Hamiltonian of $N$ interacting particles on the line is constructed using SU(1,1) as a dynamical symmetry. This hidden conformal symmetry enables us to make a group theoretic analysis of the time operator in terms of SU(1,1) generators. At distances very far from the interacting region the time operator is represented as a generalization of the quantum "time-of-arrival" operator.

quant-ph↗

arXiv2003

Spectral Statistics of RR Intervals in ECG

The statistical properties (fluctuations) of heartbeat intervals (RR intervals) in ECG are studied and compared with the predictions of Random Matrix Theory (RMT). It is found that heartbeat intervals only locally exhibit the fluctuation patterns (universality) predicted by the RMT. This finding shows that heartbeat dynamics is of the mixed type where regular and irregular (chaotic) regimes coexist and the Berry-Robnik theory can be applied. It is also observed that the distribution of heartbeat intervals is well described by the one-parameter Brody distribution. The parameter $β$ of the Brody distribution is seen to be connected with the dynamical state of the heart.

physics.med-ph↗

arXiv2002

Changes in the Hurst exponent of heartbeat intervals during physical activities

The fractal scaling properties of the heartbeat time series are studied in a controlled ergometric regime using the Hurst rescaled range R/S analysis. The long-time "memory effect" quantified by the value of the Hurst exponent $H>0.5$ is found to increase during progresive physical activity at healthy subjects in contrast to those having stable angina pectoris (SAP), where it is decreasing. We argue that this finding may be used as a useful new diagnostic parameter for short heartbeat time series.

physics.med-ph↗

arXiv2002

Is there chaos in the electron microscope?

High-temperature superconductor $Bi_{2}Sr_{2}CaCu_{2}O_{8}+x$ has been investigated by the high-resolution electron microscope (HREM) and the photodensitometric technique in order to resolve the sub-atomic shifts in the modulated structure. This investigation has shown that the background noise is pronounced, indicating some kind of ordering in certain crystallographic directions. We have found that the "mapping" of the charge densities by the inverse Fourier transform of the diffracted electron image and the connections to the crystal structure can be easily established in the case of elastically, as well as the inelastically scattered electrons. The order of the details in so obtained "inelastic" electron "micrographs", as well as the dependence of the structure of the EM image on the initial conditions of the inverse Fourier transform, leads to the conclusion that there is an order emerging from the diffuse scattered electron diffraction patterns. Data sets from digitalized densitograms are analysed by the Rescaled range (R/S) method in order to study fractal and long-range correlation properties of the inelastic scattered electrons in the "noise" region between Bragg reflections. The results of the R/S analysis showed that the value of the Hurst exponent was H$\neq$ 0.5, indicating that the "ordering" of the noise in the Inverse (Fourier) space was much more pronounced at longer distances (about 440 atom spacings), then for shorter distances of about 55 atom spacings.

nlin.CD↗

arXiv2002

Time Operator for a Quantum Singular Oscillator

The problem of existence of a self-adjoint time operator conjugate to a Hamiltonian with SU(1,1) dynamical symmetry is investigated. In the space spanned by the eigenstates of the generator $K_3$ of the SU(1,1) group, the time operator for the quantum singular harmonic potential of the form $ω^2x2 + g/x2$ is constructed explicitly, and shown that it is related to the time-of-arrival operator of Aharonov and Bohm. Our construction is fully algebraic, involving only the generators of the SU(1,1) group.

quant-ph↗

arXiv2001

Non-Linear Dynamics In Patients With Stable Angina Pectoris

We investigate the clinical and prognostic significance of fractal dimension and detrended fluctuation analysis by comparing the group of patients with stable angina pectoris without previous myocardial infarction with the group of age-matched healthy controls. The fractal dimension of the R-R series was determined using the rescaled range (R/S) analysis technique. To quantify fractal longe-range-correlation properties of heart rate variability, the detrended fluctuation analysis (DFA) technique was used. The heart rate variability was characterized by a scaling exponent $α$, separately for short-term ($<$ 11 beats), and for long-term ($>$ 11 beats) time scales. The results of data sets show the existence of crossover phenomena between short-time scales. The short-term fractal scaling exponent was significantly lower in patients with stable angina pectoris.

physics.med-ph↗

arXiv2001

Nonlinear Dynamics in the Binary DNA/RNA Coding Problem

The presence of low dimensional chaos in the protein secondary structures, using the binary coded $α$-helices and $β$-sheet motifs, has been investigated. In order to analyse symbolic DNA/RNA sequences the assignment, based on the purine/pyrimidine and strong/wea k H - bond classification sheme, of binary numbers to the nucleotides was made. We have found that this assignment leads to different averaged fractal dimensions for $α$-helices and $β$-sheets. When embedded in the two dimensional phase space the binary string structures show the attractor type behavior which depends on the value of the time lag parameter.

physics.bio-ph↗

arXiv1999

Disoriented Chiral Condensates and Anomalous Production of Pions

The leading-particle effect and the factorization property of the scattering amplitude in the impact parameter space are used to study semiclassical production of pions in the central region. The mechanism is related to the isospin-uniform solution of the nonlinear $ σ$-model coupled to quark degrees of freedom. The multipion exchange potential between two quarks is derived. It is shown thatthe soft chiral pion bremsstralung also leads to anomalously large fluctuations in the ratio of neutral to charged pions. We show that only direct production ofpions in the form of an isoscalar coherent pulse without isovector pairs can lead to large neutral-charged fluctuations.

hep-ph↗

arXiv1999

Intensity-dependent pion-nucleon coupling in multipion production processes

We propose an intensity-dependent pion-nucleon coupling Hamiltonian within a unitary multiparticle-production model of the Auerbach- Avin-Blankenbecler-Sugar (AABS) type in which the pion field is represented by the thermal-density matrix.Using this Hamiltonian, we explain the appearance of the negative-binomial (NB) distribution for pions and the well-known empirical relation, the so-called Wr\' oblewski relation, in which the dispersion $D$ of the pion- multiplicity distribution is linearly related to the average multiplicity $ $ : $D = A + B$, with the coefficient $A < 1$. The Hamiltonian of our model is expressed linearly in terms of the generators of the $SU(1,1)$ group.We also find the generating function for the pion field, which reduces to the generating function of the NB distribution limit $T \to 0$.

nucl-th↗

arXiv1995

Need for the intensity-dependent pion-nucleon coupling in multipion production processes

We give reasons in support of the use of an effective intensity-dependent pion-nucleon coupling Hamiltonian for describing the properties of the pion multiplicity distribution and the corresponding factorial moments within the thermal-density matrix approach.We explain the appearance of the negative-binomial (NB) distribution for pions and the well-known empi- rical relation of Wroblewski.Our model Hamiltonian is written as a linear combination of the generators of the SU(1,1) group.We find the generating function for the pion multiplicity distribution at finite temperature T and discuss the properties of the second-order factorial moment.Also, we show that an intensity-dependent pion-nucleon coupling generates the squeezed states of the pion field. At T=0, these squeezed states become an inherent property of the NB distribution.

hep-ph↗

arXiv1995

Intensity-dependent pion-nucleon coupling and the Wroblewski relation

We propose an intensity-dependent pion-nucleon coupling Hamiltonian within a unitary multiparticle-production model of the AABS type in which the pion field is represented by the thermal-density matrix. Using this Hamiltonian, we explain the appearance of the negative- binomial (NB) distribution for pions and the well-known empirical relation, the so-called Wroblewski relation. The Hamiltonian of our model is expressed linearly in terms of the generators of the SU(1,1) group.

hep-ph↗

arXiv1995

Isospin correlations in high-energy heavy-ion collisions

We study the posibility of large isospin fluctuations in high-energy heavy-ion collisions by assuming that pions are produced semiclassically both directly and in pairs through the isovector channel. The leading-particle effect and the factorization property of the scattering amplitude in the impact parameter space are used to define the classical pion field. In terms of the joint probability function $P_{II_{3}}(n_{0},n_{\_})$ for producing $n_{0}$ neutral and $n_{\_}$ negative pions from a definite isospin state $II_{3}$ of the incoming leading-particle system we calculate the two pion correlation parameters $f_{2,n_{\_}}^{0}$ and the average number of neutral pions $(< n_{0} >_{n_{\_}})$ as a function of negative pions $(n_{\_})$ produced. We show that only direct production of pions without isovector pairs leads to large isospin fluctuations.

hep-ph↗

arXiv1994

Can pions created in high-energy heavy-ion collisions produce a Centauro-type effect?

We study a Centauro-type phenomenon in high-energy heavy-ion collisions by assuming that pions are produced semiclassically both directly and in pairs through the isovector channel. The leading-particle effect and the factorization property of the scattering amplitude in the impact-parameter space are used to define the classical pion field. By analyzing the joint probability function $P_{II_{3}}(n_{0},n_{\_})$ for producing $n_{0}$ neutral and $n_{-}$ negative pions from a definite isospin state $II_{3}$ of the incoming leading-particle system we show that only direct production of pions without isovector pairs favors Centauro-type behavior. The presence of isovector pairs seems to destroy the effect. Our conclusion is supported through the calculation of two pion correlation parameters, $f_{2}^{0-}$ and $f_{2}^{00}$, and the average number of neutral pions $(< n_{0} >_{n_{\_}})$ as a function of negative pions $(n_{\_})$ produced.

hep-ph↗

arXiv1994

Centauro- and anti-Centauro-type events

Assuming that leading particles in high-energy hadronic and nuclear collisions become sources of a classical pion field, we show that the direct production of pions favors Centauro (mainly charged) events and that the production of pions through the $ ρ$-type channel favors anti-Centauro (mainly neutral) events. We also observe a strong negative neutral-charged correlation in both cases.

hep-ph↗