arXiv subjects
Publications and source records attributed to Salomon S. Mizrahi.
Avoiding the use of mathematical formalism, this essay exposes the quantum mechanics the phenomenon of non-locality in terms of a metaphor involving human twins focused on their hands' dexterity attribute.
Looking at the \emph{chart of nuclides} displayed at the URL of the International Atomic Energy Agency (IAEA) \cite{IAEA} -- that contains all the known nuclides, the natural and those produced artificially in labs -- one verifies the existence of two, not quite regular, \emph{delimiting lines} between which dwell all the nuclides constituting matter. These lines are established by the highly unstable radionuclides located the most far away from those in the central locus, the\emph{valley of stability}. Here, making use of the "old" semi-empirical mass formula for stable nuclides together with the energy-time uncertainty relation of quantum mechanics, by a simple calculation we show that the obtained \emph{frontier lines}, for proton and neutron excesses, present an appreciable agreement with the delimiting lines. For the sake of presenting a somewhat comprehensive panorama of the matter in our Universe and their relation with the frontier lines, we narrate, in brief, what is currently known about the astrophysical nucleogenesis processes.
We present an algorithm for the recovery of a matrix $\mathbb{M}$ % (non-singular $\in $ $\mathbb{C}^{N\times N}$) by only being aware of two of its powers, $\mathbb{M}_{k_{1}}:=\mathbb{M}^{k_{1}}$ and $\mathbb{M}% _{k_{2}}:=\mathbb{M}^{k_{2}}$ ($k_{1}>k_{2}$) whose exponents are positive coprime numbers. The knowledge of the exponents is the key to retrieve matrix $\mathbb{M}$ out from the two matrices $\mathbb{M}_{k_{i}}$. The procedure combines products and inversions of matrices, and a few computational steps are needed to get $\mathbb{M}$, almost independently of the exponents magnitudes. Guessing the matrix $\mathbb{M}$ from the two matrices $\mathbb{M}_{k_{i}}$, without the knowledge of $k_{1}$ and $k_{2}$, is comparatively highly consuming in terms of number of operations. If a private message, contained in $\mathbb{M}$, has to be conveyed, the exponents can be encrypted and then distributed through a public key method as, for instance, the DF (Diffie-Hellman), the RSA (Rivest-Shamir-Adleman), or any other.
We propose three models for the traffic of vehicles within a network formed by sites (cities, car-rental agencies, parking lots, etc.) and connected by two-way arteries (roads, highways), that allow forecasting the vehicular flux in a sequence of $n$ consecutive steps, or units of time. An essential approach consists in using, as an "a priori" information, previous observations and measurements. The formal tools used in our analysis consists in: (1) associating a digraph to the network where the edges correspond to arteries and the vertices with loops represent the sites. (2) From an initial set of numbers, that are the distribution of vehicles within the network, we construct a matrix that we transform into a stochastic matrix (SM) by normalizing the rows, whose entries are now transition probabilities. This matrix becomes the generator of the evolution of the traffic flow. And (3), we use the Perron-Frobenius theory for a formal analysis. We investigate three models: (a) a closed four-site network having a conserved number of vehicles; (b) to this network we add an influx and an outflux of vehicles to characterize an open system; asymptotically, $n \rightarrow \infty$, the SM raised to the power $n$ goes to a unique stationary matrix. And (c), we construct a nonlinear model because the formal structure permits the existence of several ($L$) stationary states for the distribution of vehicles at each site, that alternate cyclically with time. Each state represents the traffic for $L$ different moments. These models were used to analyze the traffic in a sector of the city of Tigre, located in the province of Buenos Aires, Argentina. The results are presented in a following paper.
The entanglement between $SU(2) \otimes SU(2)$ internal degrees of freedom of parity and helicity for reflected and transmitted waves of Dirac-like particles scattered by a potential step along an arbitrary direction on the $x-y$ plane is quantified. Diffusion ($E \geq V$) and Klein zone ($V \geq E$) energy regimes are considered. It has been shown that, for $SU(2) \otimes SU(2)$ polarized structures of helicity eigenstates impinging the barrier, the local interaction with a {\em step} potential destroys the {\em parity-spin} separability. The framework presented here can be straightforwardly translated into a useful theoretical tool for obtaining the {\em spin-spin} entanglement in the context of enlarged scenarios of nonrelativistic $2D$ systems, as for instance those for describing single layer graphene, or even single trapped ions with Dirac bi-spinor mathematical structure.
The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard billiards is obtained and their components behavior are monitored in time. It is assumed that the independent degrees of freedom are two \emph{free} 1D harmonic oscillators (HO's), so the system Hamiltonian does not contain interaction terms. Through the noncommutative deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained Hamiltonian represents then two \emph{interacting} 1D HO's. By assuming that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed in terms of Wigner functions, which are essential to put in evidence the effects of the noncommutativity.
Dirac equation describes the dynamics of a relativistic spin-1/2 particle regarding its spatial motion and intrinsic degrees of freedom. Here we adopt the point of view that the spinors describe the state of a massive particle carrying two qubits of information: helicity and intrinsic parity. We show that the density matrix for a gas of free fermions, in thermal equilibrium, correlates helicity and intrinsic parity. Our results introduce the basic elements for discussing the spin-parity correlation for a Fermi gas: (1) at the ultra-relativistic domains, when the temperature is quite high, $T > 10^{10}\ K$, the fermions have no definite intrinsic parity (50% : 50%), which is maximally correlated with the helicity; (2) at very low temperature, $T \approx 3 \ K$, a unique parity dominates (conventionally chosen positive), by $10^{20}$ to $1$, while the helicity goes into a mixed state for spin up and down, and the quantum correlation decoheres. For the anti-fermions we get the opposite behavior. In the framework of quantum information, our result could be considered as a plausible explanation of why we do accept, as a fact (consistent with the experimental observation), that fermions (and anti-fermions), in our present epoch of a cool universe, have a unique intrinsic parity. The framework for constructing spin-parity entangled states is established.
The relation between the symplectic and Lorentz groups is explored to investigate entanglement features in a two-mode bipartite Gaussian state. We verify that the correlation matrix of arbitrary Gaussian states can be associated to a hyperbolic space with a Minkowski metric, which is divided in two regions - separablelike and entangledlike, in equivalence to timelike and spacelike in special relativity. This correspondence naturally allows the definition of two insightful invariant squared distances measures - one related to the purity and another related to amount of entanglement. The second distance allows us to define a measure for entanglement in terms of the invariant interval between the given state and its closest separable state, given in a natural manner without the requirement of a minimization procedure.
Here I show that a classical or quantum bit state plus one simple operation, an action, are sufficient ingredients to derive a quantum dynamical equation that rules the sequential changes of the state. Then, by assuming that a freely moving massive particle is the qubit carrier, it is found that both, the particle position in physical space and the qubit state, change in time according to the Pauli-Schroedinger equation. So, this approach suggests the following conjecture: because it carries one qubit of information the particle motion has its description enslaved by the very existence of the internal degree of freedom. It is compelled to be no more described classically but by a wavefunction. I also briefly discuss the Dirac equation in terms of qubits.
We propose three schemes to engineer 2^M and M+1 circular states for the motion of the center of mass of a trapped ion, $M$ being the number of laser pulses. Since the ion is subjected to several laser pulses, we analyze the necessary duration of each one for generating the circular states, and from these, the Fock states and superposition of two-Fock states. We also calculate the probability for obtaining the required states.
Here we consider the Husimi function P for the squeezed states and calculate the marginal and correlation distribution functions when P is projected onto the photon number states. According to the value of the squeezing parameter one verifies the occurence of oscillations and beats as already appointed in the literature. We verify that these phenomena are entirely contained in the correlation function. In particular, we show that since Husimi and its marginal distribution functions satisfy partial differential equations where the squeeze parameter plays the role of time, the solutions (the squeezed functions obtained from initial unsqueezed functions) can be expressed by means of kernels responsible for the propagation of squeezing. From the calculational point of view, this method presents advantages for calculating the marginal distribution functions (compared to a direct integration over one of the two phase-space variables of P) since one can use the symmetry properties of the differential equations.