A method for making relativistic non-quantum systems by constructing the Hamiltonian and the other nine generating functions

2005 ◽  
pp. 312-314
Author(s):  
Richard Arens
Keyword(s):  
Generating Functions ◽  
Quantum Systems ◽  
The Other

scholarly journals Multi-Bloch vector representation of the qutrit

2011 ◽  
Vol 11 (5&6) ◽  
pp. 361-373
Author(s):  
Pawel Kurzynski
Keyword(s):  
Quantum State ◽  
Quantum Systems ◽  
Quantum States ◽  
The Other ◽  
Two Dimensional ◽  
Bloch Vector ◽  
Vector Representation ◽  
Alternative Approach ◽  
Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

Duels, Truels, Gruels, and Survival of the Unfittest

2017 ◽  
Author(s):  
Dominic Lanphier
Keyword(s):  
Generating Functions ◽  
The Other ◽  
Main Issue ◽  
Basic Facts ◽  
Combinatorial Methods

This chapter considers two generalizations of duels. The first generalization is to n players, like n-uels. The other generalization is an iterative duel. The main issue for both of these duel-type games is to determine the likelihood that a player will survive the game. Section 1 reviews the main definitions, rules, and results about (sequential) duels and truels. Section 2 introduces duel-type games called gruels, giving some simple examples and establishing certain basic facts concerning such games. Section 3 introduces the second generalization, iterative duels. It applies certain combinatorial methods to investigate these games. In particular, it applies generating functions and thereby obtains arithmetic results about numbers associated to such duels. Section 4 applies more delicate analysis. This section is more mathematically challenging and follows methods from Stanley and Wilf to study which player in a sequential iterative duel is most likely to win.

A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS

2005 ◽  
Vol 01 (02) ◽  
pp. 175-182 ◽  
Author(s):  
CHANDRASHEKAR ADIGA ◽  
SHAUN COOPER ◽  
JUNG HUN HAN
Keyword(s):  
Generating Functions ◽  
General Relation ◽  
The Other ◽  
Sums Of Squares ◽  
Triangular Numbers

Let rk(n) and tk(n) denote the number of representations of n as a sum of k squares, and as a sum of k triangular numbers, respectively. We give a generalization of the result rk(8n + k) = cktk(n), which holds for 1 ≤ k ≤ 7, where ck is a constant that depends only on k. Two proofs are provided. One involves generating functions and the other is combinatorial.

scholarly journals Generating functions for two-variable polynomials related to a family of Fibonacci type polynomials and numbers

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 969-975 ◽  
Author(s):  
Gulsah Ozdemir ◽  
Yilmaz Simsek
Keyword(s):  
Infinite Series ◽  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Functional Equations ◽  
The Other ◽  
The Family

The purpose of this paper is to construct generating functions for the family of the Fibonacci and Jacobsthal polynomials. Using these generating functions and their functional equations, we investigate some properties of these polynomials. We also give relationships between the Fibonacci, Jacobsthal, Chebyshev polynomials and the other well known polynomials. Finally, we give some infinite series applications related to these polynomials and their generating functions.

scholarly journals Coupling modifies the quantum fluctuations of entangled oscillators

2021 ◽  
Author(s):  
Roberto Baginski Batista Santos ◽  
Vinicius de Souza Ferreira Lisboa
Keyword(s):  
Coupled Oscillators ◽  
Quantum Fluctuations ◽  
Quantum Systems ◽  
Transfer Mechanism ◽  
The Other ◽  
Precision Measurements ◽  
Uncertainty Product

Abstract Coupled oscillators are among the simplest composite quantum systems in which the interplay of entanglement and interaction may be explored. We examine the effects of coupling on the quantum fluctuations of the coordinates and momenta of the oscillators in a single-excitation entangled Bell-like state. We discover that coupling acts as a mechanism for noise transfer between one pair of coordinate and momentum and another. Through this noise transfer mechanism, the uncertainty product is lowered, on average, relatively to its non-coupled level for one pair of coordinate and momentum and it is enhanced for the other pair. This novel mechanism for noise transfer may be explored in precision measurements in entanglement-assisted sensing and metrology.

scholarly journals Quantum Horn's lemma, finite heat baths, and the third law of thermodynamics

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 54 ◽  
Author(s):  
Jakob Scharlau ◽  
Markus P. Mueller
Keyword(s):  
Crucial Role ◽  
Heat Bath ◽  
Quantum Systems ◽  
The Other ◽  
State Transitions ◽  
Quantum Operations ◽  
The Third ◽  
Third Law Of Thermodynamics ◽  
Quantum Version ◽  
Third Law

Interactions of quantum systems with their environment play a crucial role in resource-theoretic approaches to thermodynamics in the microscopic regime. Here, we analyze the possible state transitions in the presence of "small" heat baths of bounded dimension and energy. We show that for operations on quantum systems with fully degenerate Hamiltonian (noisy operations), all possible state transitions can be realized exactly with a bath that is of the same size as the system or smaller, which proves a quantum version of Horn's lemma as conjectured by Bengtsson and Zyczkowski. On the other hand, if the system's Hamiltonian is not fully degenerate (thermal operations), we show that some possible transitions can only be performed with a heat bath that is unbounded in size and energy, which is an instance of the third law of thermodynamics. In both cases, we prove that quantum operations yield an advantage over classical ones for any given finite heat bath, by allowing a larger and more physically realistic set of state transitions.

CLASSES OF MRM-APPLICABLE MEASURES FOR THE POWER FUNCTION OF GENERAL ORDER

2013 ◽  
Vol 16 (04) ◽  
pp. 1350028
Author(s):  
IZUMI KUBO ◽  
HUI-HSIUNG KUO ◽  
SUAT NAMLI
Keyword(s):  
Orthogonal Polynomials ◽  
Power Function ◽  
Generating Functions ◽  
The Other ◽  
Large Classes ◽  
Beta Distributions ◽  
General Order ◽  
Multiplicative Renormalization ◽  
Renormalization Method ◽  
Special Classes

The authors have previously studied multiplicative renormalization method (MRM) for generating functions of orthogonal polynomials. In particular, they have determined all MRM-applicable measures for renormalizing functions h(x) = ex, h(x) = (1 - x)-κ, κ = 1/2, 1, 2. For the cases h(x) = ex and (1 - x)-1, there are very large classes of MRM-applicable measures. For the other two cases κ = 1/2, 2, MRM-applicable measures belong to special classes of a certain kind of beta distributions. In this paper, we determine all MRM-applicable measures for h(x) = (1 - x)-κ with κ ≠ 0, 1, 1/2.

scholarly journals Quantum Entropy and Complexity

2017 ◽  
Vol 24 (02) ◽  
pp. 1750005
Author(s):  
F. Benatti ◽  
S. Khabbazi Oskouei ◽  
A. Shafiei Deh Abad
Keyword(s):  
Dynamical Systems ◽  
Shannon Entropy ◽  
Kolmogorov Complexity ◽  
Quantum Systems ◽  
Quantum Spin ◽  
Spin Chains ◽  
The Other ◽  
Quantum Entropy ◽  
Quantum Spin Chains ◽  
Quantum Complexity

We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs [1] and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A. A. Brudno [2]. On the other hand, using the quantum Shannon-McMillan theorem [3], we show that such an equality holds densely in the case of ergodic quantum spin chains.

FEEDBACK IN OPEN QUANTUM SYSTEMS

1995 ◽  
Vol 09 (11n12) ◽  
pp. 629-654 ◽  
Author(s):  
H. M. WISEMAN
Keyword(s):  
System Dynamics ◽  
Feedback Loop ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Feedback Mechanism ◽  
The Other ◽  
Langevin Equations ◽  
Quantum Trajectories ◽  
Classical Counterpart ◽  
Open Quantum

Open quantum systems continually lose information to their surroundings. In some cases this information can be readily retrieved from the environment and put to good use by engineering a feedback loop to control the system dynamics. Two cases are distinguished: one where the feedback mechanism involves a measurement of the environment, and the other where no measurement is made. It is shown that the latter case can always replicate the former, but not vice versa. This emphasizes the quantum nature of the information being fed back. Two approaches are used to describe the feedback: quantum trajectories (which apply only for feedback based on measurement) and quantum Langevin equations (which can be used in either case), and the results are shown to be equivalent. The obvious applications for the theory are in quantum optics, where the information is lost by radiation damping and can be retrieved by photodetection. A few examples are discussed, one of which is particularly interesting as it has no classical counterpart.

scholarly journals Some Polynomial Sequence Relations

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 750 ◽  
Author(s):  
Chan-Liang Chung
Keyword(s):  
Generating Functions ◽  
The Other ◽  
Polynomial Sequence ◽  
Elementary Identity

We give some polynomial sequence relations that are generalizations of the Sury-type identities. We provide two proofs, one based on an elementary identity and the other using the method of generating functions.

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