1,352 research outputs found
Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
Nonlinear SUSY approach to preparation of quantum systems with pre-planned
spectral properties is reviewed. Possible multidimensional extensions of
Nonlinear SUSY are described. The full classification of ladder-reducible and
irreducible chains of SUSY algebras in one-dimensional QM is given. Emergence
of hidden symmetries and spectrum generating algebras is elucidated in the
context of Nonlinear SUSY in one- and two-dimensional QM.Comment: 75 pages, Minor corrections, Version published in Journal of Physics
Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
We study the phase diagram of a one-dimensional balls-in-boxes (BIB) model
that has been proposed as an effective model for the spatial-volume dynamics of
(2+1)-dimensional causal dynamical triangulations (CDT). The latter is a
statistical model of random geometries and a candidate for a nonperturbative
formulation of quantum gravity, and it is known to have an interesting phase
diagram, in particular including a phase of extended geometry with classical
properties. Our results corroborate a previous analysis suggesting that a
particular type of potential is needed in the BIB model in order to reproduce
the droplet condensation typical of the extended phase of CDT. Since such a
potential can be obtained by a minisuperspace reduction of a (2+1)-dimensional
gravity theory of the Ho\v{r}ava-Lifshitz type, our result strengthens the link
between CDT and Ho\v{r}ava-Lifshitz gravity.Comment: 21 pages, 7 figure
On Jordan's measurements
The Jordan measure, the Jordan curve theorem, as well as the other generic
references to Camille Jordan's (1838-1922) achievements highlight that the
latter can hardly be reduced to the "great algebraist" whose masterpiece, the
Trait\'e des substitutions et des equations alg\'ebriques, unfolded the
group-theoretical content of \'Evariste Galois's work. The present paper
appeals to the database of the reviews of the Jahrbuch \"uber die Fortschritte
der Mathematik (1868-1942) for providing an overview of Jordan's works. On the
one hand, we shall especially investigate the collective dimensions in which
Jordan himself inscribed his works (1860-1922). On the other hand, we shall
address the issue of the collectives in which Jordan's works have circulated
(1860-1940). Moreover, the time-period during which Jordan has been publishing
his works, i.e., 1860-1922, provides an opportunity to investigate some
collective organizations of knowledge that pre-existed the development of
object-oriented disciplines such as group theory (Jordan-H\"older theorem),
linear algebra (Jordan's canonical form), topology (Jordan's curve), integral
theory (Jordan's measure), etc. At the time when Jordan was defending his
thesis in 1860, it was common to appeal to transversal organizations of
knowledge, such as what the latter designated as the "theory of order." When
Jordan died in 1922, it was however more and more common to point to
object-oriented disciplines as identifying both a corpus of specialized
knowledge and the institutionalized practices of transmissions of a group of
professional specialists
Two-Point Functions and Boundary States in Boundary Logarithmic Conformal Field Theories
Our main aim in this thesis is to address the results and prospects of
boundary logarithmic conformal field theories: theories with boundaries that
contain the above Jordan cell structure. We have investigated c_{p,q} boundary
theory in search of logarithmic theories and have found logarithmic solutions
of two-point functions in the context of the Coulomb gas picture. Other
two-point functions have also been studied in the free boson construction of
BCFT with SU(2)_k symmetry. In addition, we have analyzed and obtained the
boundary Ishibashi state for a rank-2 Jordan cell structure [hep-th/0103064].
We have also examined the (generalised) Ishibashi state construction and the
symplectic fermion construction at c=-2 for boundary states in the context of
the c=-2 triplet model. The differences between two constructions are
interpreted, resolved and extended beyond each case.Comment: Ph.D. Thesis (University of Oxford), 96 pages, the layout is modified
from the origina
Effective Non-Hermiticity and Topology in Markovian Quadratic Bosonic Dynamics
Recently, there has been an explosion of interest in re-imagining many-body quantum phenomena beyond equilibrium. One such effort has extended the symmetry-protected topological (SPT) phase classification of non-interacting fermions to driven and dissipative settings, uncovering novel topological phenomena that are not known to exist in equilibrium which may have wide-ranging applications in quantum science. Similar physics in non-interacting bosonic systems has remained elusive. Even at equilibrium, an effective non-Hermiticity intrinsic to bosonic Hamiltonians poses theoretical challenges. While this non-Hermiticity has been acknowledged, its implications have not been explored in-depth. Beyond this dynamical peculiarity, major roadblocks have arisen in the search for SPT physics in non-interacting bosonic systems, calling for a much needed paradigm shift beyond equilibrium.
The research program undertaken in this thesis provides a systematic investigation of effective non-Hermiticity in non-interacting bosonic Hamiltonians and establishes the extent to which one must move beyond equilibrium to uncover SPT-like bosonic physics. Beginning in the closed-system setting, whereby systems are modeled by quadratic Hamiltonians, we classify the types of dynamical instabilities effective non-Hermiticity engenders. While these flavors of instability are distinguished by the algebraic behavior of normal modes, they can be unified under the umbrella of spontaneous generalized parity-time symmetry-breaking. By harnessing tools from Krein stability theory, a numerical indicator of dynamical stability phase transitions is also introduced. Throughout, the role played by non-Hermiticity in dynamically stable systems is scrutinized, resulting in the discovery of a Hermiticity-restoring duality transformation.
Building on the preceding analysis, we take the necessary plunge into open bosonic systems undergoing Markovian dissipation, modeled by quadratic (Gaussian) Lindblad master equations. The first finding is that of a uniquely-bosonic notion of dynamical metastability, whereby asymptotically stable dynamics are preempted by a regime of transient amplification. Incorporating non-trivial topological invariants leads to the notion of topological metastability which, remarkably, features tight bosonic analogues to the edge modes characteristic of fermionic SPT phases - which we deem Majorana and Dirac bosons - along with a manifold of long-lived quasi-steady states. Implications regarding the breakdown of Noether\u27s theorem are explored, and several observable signatures based on two-time correlation functions and power spectra are proposed
Nonperturbative Quantum Gravity
Asymptotic safety describes a scenario in which general relativity can be
quantized as a conventional field theory, despite being nonrenormalizable when
expanding it around a fixed background geometry. It is formulated in the
framework of the Wilsonian renormalization group and relies crucially on the
existence of an ultraviolet fixed point, for which evidence has been found
using renormalization group equations in the continuum.
"Causal Dynamical Triangulations" (CDT) is a concrete research program to
obtain a nonperturbative quantum field theory of gravity via a lattice
regularization, and represented as a sum over spacetime histories. In the
Wilsonian spirit one can use this formulation to try to locate fixed points of
the lattice theory and thereby provide independent, nonperturbative evidence
for the existence of a UV fixed point.
We describe the formalism of CDT, its phase diagram, possible fixed points
and the "quantum geometries" which emerge in the different phases. We also
argue that the formalism may be able to describe a more general class of
Ho\v{r}ava-Lifshitz gravitational models.Comment: Review, 146 pages, many figure
Periodic-orbit approach to the nuclear shell structures with power-law potential models: Bridge orbits and prolate-oblate asymmetry
Deformed shell structures in nuclear mean-field potentials are systematically
investigated as functions of deformation and surface diffuseness. As the
mean-field model to investigate nuclear shell structures in a wide range of
mass numbers, we propose the radial power-law potential model, V \propto
r^\alpha, which enables a simple semiclassical analysis by the use of its
scaling property. We find that remarkable shell structures emerge at certain
combinations of deformation and diffuseness parameters, and they are closely
related to the periodic-orbit bifurcations. In particular, significant roles of
the "bridge orbit bifurcations" for normal and superdeformed shell structures
are pointed out. It is shown that the prolate-oblate asymmetry in deformed
shell structures is clearly understood from the contribution of the bridge
orbit to the semiclassical level density. The roles of bridge orbit
bifurcations in the emergence of superdeformed shell structures are also
discussed.Comment: 20 pages, 23 figures, revtex4-1, to appear in Phys. Rev.
Transport in deformed centrosymmetric networks
Centrosymmetry often mediates Perfect State Transfer (PST) in various complex
systems ranging from quantum wires to photosynthetic networks. We introduce the
Deformed Centrosymmetric Ensemble (DCE) of random matrices, , where is centrosymmetric while is
skew-centrosymmetric. The relative strength of the prompts the system
size scaling of the control parameter as . We
propose two quantities, and , quantifying centro-
and skewcentro-symmetry, respectively, exhibiting second order phase
transitions at and . In
addition, DCE posses an ergodic transition at . Thus
equipped with a precise control of the extent of centrosymmetry in DCE, we
study the manifestation of on the transport properties of complex
networks. We propose that such random networks can be constructed using the
eigenvectors of and establish that the maximum transfer fidelity,
, is equivalent to the degree of centrosymmetry, .Comment: 13 pages, 5 figure
Exactly solvable path integral for open cavities in terms of quasinormal modes
We evaluate the finite-temperature Euclidean phase-space path integral for
the generating functional of a scalar field inside a leaky cavity. Provided the
source is confined to the cavity, one can first of all integrate out the fields
on the outside to obtain an effective action for the cavity alone.
Subsequently, one uses an expansion of the cavity field in terms of its
quasinormal modes (QNMs)-the exact, exponentially damped eigenstates of the
classical evolution operator, which previously have been shown to be complete
for a large class of models. Dissipation causes the effective cavity action to
be nondiagonal in the QNM basis. The inversion of this action matrix inherent
in the Gaussian path integral to obtain the generating functional is therefore
nontrivial, but can be accomplished by invoking a novel QNM sum rule. The
results are consistent with those obtained previously using canonical
quantization.Comment: REVTeX, 26 pages, submitted to Phys. Rev.
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