Spelling suggestions: "subject:"kuantum systems"" "subject:"auantum systems""
31 |
G-CONSISTENT SUBSETS AND REDUCED DYNAMICAL QUANTUM MAPSCeballos, Russell R. 01 August 2017 (has links)
A quantum system which evolves in time while interacting with an external environ- ment is said to be an open quantum system (OQS), and the influence of the environment on the unperturbed unitary evolution of the system generally leads to non-unitary dynamics. This kind of open system dynamical evolution has been typically modeled by a Standard Prescription (SP) which assumes that the state of the OQS is initially uncorrelated with the environment state. It is here shown that when a minimal set of physically motivated assumptions are adopted, not only does there exist constraints on the reduced dynamics of an OQS such that this SP does not always accurately describe the possible initial cor- relations existing between the OQS and environment, but such initial correlations, and even entanglement, can be witnessed when observing a particular class of reduced state transformations termed purity extractions are observed. Furthermore, as part of a more fundamental investigation to better understand the minimal set of assumptions required to formulate well defined reduced dynamical quantum maps, it is demonstrated that there exists a one-to-one correspondence between the set of initial reduced states and the set of admissible initial system-environment composite states when G-consistency is enforced. Given the discussions surrounding the requirement of complete positivity and the reliance on the SP, the results presented here may well be found valuable for determining the ba- sic properties of reduced dynamical maps, and when restrictions on the OQS dynamics naturally emerge.
|
32 |
Unital dilations of completely positive semigroupsGaebler, David 01 May 2013 (has links)
Semigroups of completely positive maps arise naturally both in noncommutative stochastic processes and in the dynamics of open quantum systems. Since its inception in the 1970's, the study of completely positive semigroups has included among its central topics the dilation of a completely positive semigroup to an endomorphism semigroup. In quantum dynamics, this amounts to embedding a given open system inside some closed system, while in noncommutative probability, it corresponds to the construction of a Markov process from its transition probabilities. In addition to the existence of dilations, one is interested in what properties of the original semigroup (unitality, various kinds of continuity) are preserved.
Several authors have proved the existence of dilations, but in general, the dilation achieved has been non-unital; that is, the unit of the original algebra is embedded as a proper projection in the dilation algebra. A unique approach due to Jean-Luc Sauvageot overcomes this problem, but leaves unclear the continuity of the dilation semigroup. The major purpose of this thesis, therefore, is to further develop Sauvageot's theory in order to prove the existence of continuous unital dilations. This existence is proved in Theorem 6.4.9, the central result of the thesis.
The dilation depends on a modification of free probability theory, and in particular on a combinatorial property akin to free independence. This property is implicit in some Sauvageot's original calculations, but a secondary goal of this thesis is to present it as its own object of study, which we do in chapter 3.
|
33 |
Classical Reduction of Quantum Master Equations as Similarity Transformation / 相似変換としての量子マスター方程式の古典化Kamiya, Norikazu 23 March 2015 (has links)
京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18776号 / 理博第4034号 / 新制||理||1581(附属図書館) / 31727 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 武末 真二, 教授 佐々 真一, 教授 早川 尚男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM
|
34 |
Analytic representations of quantum systems with Theta functionsEvangelides, Pavlos January 2015 (has links)
Quantum systems in a d-dimensional Hilbert space are considered, where
the phase spase is Z(d) x Z(d). An analytic representation in a cell S in the
complex plane using Theta functions, is defined. The analytic functions have
exactly d zeros in a cell S. The reproducing kernel plays a central role in
this formalism. Wigner and Weyl functions are also studied.
Quantum systems with positions in a circle S and momenta in Z are also
studied. An analytic representation in a strip A in the complex plane is also
defined. Coherent states on a circle are studied. The reproducing kernel is
given. Wigner and Weyl functions are considered.
|
35 |
Partial ordering of weak mutually unbiased bases in finite quantum systemsOladejo, Semiu Oladipupo January 2015 (has links)
There has being an enormous work on finite quantum systems with variables in Zd, especially on mutually unbiased bases. The reason for this is due to its
wide areas of application. We focus on partial ordering of weak mutually un-biased bases. In it, we studied a partial ordered relation which exists between a subsystem ^(q) and a larger system ^(d) and also, between a subgeometry Gq and larger geometry Gd. Furthermore, we show an isomorphism between:
(i) the set {Gd} of subgeometries of a finite geometry Gd and subsets of the set {D(d)} of divisors of d.
(ii) the set {hd} of subspaces of a finite Hilbert space Hd and subsets of the set {D(d)} of divisors of d.
(iii) the set {Y(d)} of subsystems of a finite quantum system ^(d) and subsets of the set {D(d)} of divisors of d.
We conclude this work by showing a duality between lines in finite geometry Gd and weak mutually unbiased bases in finite dimensional Hilbert space Hd.
|
36 |
Quantum correlations and measurements in tri-partite quantum systems.Idrus, Bahari bin January 2011 (has links)
Correlations and entanglement in a chain of three oscillators A,B,C with
nearest neighbour coupling is studied. Oscillators A,B and B,C are coupled
but there is no direct coupling between oscillators A,C. Examples with initial
factorizable states are considered, and the time evolution is calculated. It
is shown that the dynamics of the tri-partite system creates correlations and
entanglement among the three oscillators and in particular, between oscillators
A,C which are not coupled directly. We have performed photon number
selective and non-selective measurements on oscillator A and we investigated
their effects on the correlations and entanglement. It is shown that, before
the measurement, the correlations between oscillators A,C can be stronger
than the correlations of oscillators A,B. Moreover, some entanglement witness
shows that oscillators A,C are entangled but the oscillators A,B might
or might not be entangled. By using quantum discord, which measures the
quantumness of correlations, it is shown that there are quantum correlations
between oscillators A,B and after the measurements in both cases of selective
and non-selective measurements, oscillators A,B and A,C become classically
correlated. / Ministry of Higher Education, Malaysia and Universiti Kebangsaan, Malaysia.
|
37 |
Unitarily inequivalent local and global Fourier transforms in multipartite quantum systemsLei, Ci, Vourdas, Apostolos 23 January 2023 (has links)
Yes / A multipartite system comprised of n subsystems, each of which is described with
‘local variables’ in Z(d) and with a d-dimensional Hilbert space H(d), is considered.
Local Fourier transforms in each subsystem are defined and related phase space methods are discussed (displacement operators, Wigner and Weyl functions, etc). A holistic
view of the same system might be more appropriate in the case of strong interactions,
which uses ‘global variables’ in Z(dn) and a dn-dimensional Hilbert space H(dn).
A global Fourier transform is then defined and related phase space methods are discussed. The local formalism is compared and contrasted with the global formalism.
Depending on the values of d, n the local Fourier transform is unitarily inequivalent
or unitarily equivalent to the global Fourier transform. Time evolution of the system
in terms of both local and global variables, is discussed. The formalism can be useful
in the general area of Fast Fourier transforms.
|
38 |
Lower and upper probabilities in the distributive lattice of subsystemsVourdas, Apostolos 07 July 2014 (has links)
yes / The set of subsystems ∑ (m) of a finite quantum system ∑(n) (with variables in Ζ(n)) together with logical connectives, is a distributive lattice. With regard to this lattice, the ℓ(m | ρn) = Tr (𝔓(m) ρn ) (where 𝔓(m) is the projector to ∑(m)) obeys a supermodularity inequality, and it is interpreted as a lower probability in the sense of the Dempster–Shafer theory, and not as a Kolmogorov probability. It is shown that the basic concepts of the Dempster–Shafer theory (lower and upper probabilities and the Dempster multivaluedness) are pertinent to the quantum formalism of finite systems.
|
39 |
Beyond the Exceptional Point: Exploring the Features of Non-Hermitian PT Symmetric SystemsAgarwal, Kaustubh Shrikant 08 1900 (has links)
Indiana University-Purdue University Indianapolis (IUPUI) / Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semi-classical models with mode selective losses, and lossy quantum systems. The rapidly growing research on these systems has mainly focused on the wide range of novel functionalities they demonstrate. In this thesis, I intend to present some intriguing properties of a class of open systems which possess parity (P) and time-reversal (T) symmetry with a theoretical background, accompanied by the experimental platform these are realized on. These systems show distinct regions of broken and unbroken symmetries separated by a special phase boundary in the parameter space. This separating boundary is called the PT-breaking threshold or the PT transition threshold.
We investigate non-Hermitian systems in two settings: tight binding lattice models, and electrical circuits, with the help of theoretical and numerical techniques.
With lattice models, we explore the PT-symmetry breaking threshold in discrete realizations of systems with balanced gain and loss which is determined by the effective coupling between the gain and loss sites. In one-dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains, and find that it is increased by a factor proportional to the number of neutral chains. These results provide a surprising way to engineer the PT threshold in experimentally accessible samples.
In another example, we investigate the PT-threshold for a one-dimensional, finite Kitaev chain—a prototype for a p-wave superconductor— in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, onsite potential, and the distance between the gain and loss sites. In addition to a robust, non-local
threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev model.
Finally, with electrical circuits, we propose a protocol to study the properties of a PT-symmetric system in a single LC oscillator circuit which is contrary to the notion that these systems require a pair of spatially separated balanced gain and loss elements. With a dynamically tunable LC oscillator with synthetically constructed circuit elements, we demonstrate static and
Floquet PT breaking transitions by tracking the energy of the circuit. Distinct from traditional mechanisms to implement gain and loss, our protocol enables parity-time symmetry in a minimal classical system.
|
40 |
An analytic function approach to weak mutually unbiased basesOlupitan, Tominiyi E., Lei, Ci, Vourdas, Apostolos 01 June 2017 (has links)
yes / Quantum systems with variables in Z(d) are considered, and three different structures are studied. The first is weak mutually unbiased bases, ... The second is maximal lines through the origin in the Z(d)×Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. For simplicity, the case where d=p1×p2, where p1,p2 are odd prime numbers different from each other, is considered. / The full text will be available 12 months after publication
|
Page generated in 0.6565 seconds