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1.
With the advent of medium and large gamma detector arrays, it is now possible to look at nuclear structure at high rotational
forces. The role of pairing correlations and their eventual breakdown, along with the shell effects have showed us the interesting
physics for nuclei at high spins — superdeformation, shape co-existence, yrast traps, alignments and their dramatic effects
on nuclear structure and so on. Nuclear structure studies have recently become even more exciting, due to efforts and possibilities
to reach nuclei far off from the stability valley. Coupling of gamma ray arrays with ‘filters’, like neutron wall, charged
particle detector array, gamma ray total energy and multiplicity castles, conversion electron spectrometers etc gives a great
handle to study nuclei produced online with ‘low’ cross-sections. Recently we studied, nuclei in mass region 80 using an array
of 8 germanium detectors in conjunction with the recoil mass analyser, HIRA at the Nuclear Science Centre and, most unexpectedly
came across the phenomenon of identical bands, with two quasi-particle difference. The discovery of magnetic rotation is another
highlight. Our study of light In nucleus, 107In brought us face to face with the ‘dipole’ bands. I plan to discuss some of
these aspects. There is also an immensely important development — that of the ‘radioactive ion beams’. The availability of
RIB, will probably very dramatically influence our ‘conventional’ concept of nuclear structure. The exotic shapes of these
exotic nuclei and some of their expected properties will also be touched upon. 相似文献
2.
M. Günaydin A. Neitzke O. Pavlyk B. Pioline 《Communications in Mathematical Physics》2008,283(1):169-226
Quasi-conformal actions were introduced in the physics literature as a generalization of the familiar fractional linear action on the upper half plane, to Hermitian symmetric tube domains based on arbitrary Jordan algebras, and further to arbitrary Freudenthal triple systems. In the mathematics literature, quaternionic discrete series unitary representations of real reductive groups in their quaternionic real form were constructed as degree 1 cohomology on the twistor spaces of symmetric quaternionic-Kähler spaces. These two constructions are essentially identical, as we show explicitly for the two rank 2 cases SU(2, 1) and G 2(2). We obtain explicit results for certain principal series, quaternionic discrete series and minimal representations of these groups, including formulas for the lowest K-types in various polarizations. We expect our results to have applications to topological strings, black hole micro-state counting and to the theory of automorphic forms. 相似文献
3.
A P Balachandran 《Pramana》2001,56(2-3):223-237
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators
are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major
axiom in quantum physics than those formulated for example in Dirac’s ‘quantum mechanics’, then a quantum physicist would
not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with
smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and
with further refinements of the axiom, its C
K - and C
--structures) can be reconstructed using Gel’fand-Naimark theory and its extensions. Classical topology is an attribute of
only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less
differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating
these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental
issues concerning the role of time in quantum physics are also addressed. 相似文献
4.
We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ‘infinite’,
Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into
single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and
algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct
many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are: new
algebras for infinite statistics,q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen
order, ‘doubly-infinite’ statistics, many representations of orthostatistics, Hubbard statistics and its variations. 相似文献
5.
Sushanta Dattagupta 《Pramana》2002,59(2):203-219
We present an ‘overview’ of coherence-to-decoherence transition in certain selected problems of condensed matter physics.
Our treatment is based on a subsystem-plus-environment approach. All the examples chosen in this paper have one thing in common
— the environmental degrees of freedom are taken to be bosonic and their spectral density of excitations is assumed to be
‘ohmic’. The examples are drawn from a variety of phenomena in condensed matter physics involving, for instance, quantum diffusion
of hydrogen in metals, Landau diamagnetism and c-axis transport in high T
c superconductors. 相似文献
6.
Considering the fundamental role symmetry plays throughout physics, it is remarkable how little attention has been paid to
it in the quantum-logical literature. In this paper, we discuss G-test spaces—that is, test spaces hosting an action by a group G—and their logics. The focus is on G-test spaces having strong homogeneity properties. After establishing some general results and exhibiting various specimens
(some of them exotic), we show that a sufficiently symmetric G-test space having an invariant, separating set of states with affine dimension n, is always representable in terms of a real Hilbert space of dimension n+1, in such a way that orthogonal outcomes are represented by orthogonal unit vectors. 相似文献
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9.
Peter Mittelstaedt 《International Journal of Theoretical Physics》2008,47(1):104-113
The goal of quantum logic is the “bottom-top” reconstruction of quantum mechanics. Starting from a weak quantum ontology,
a long sequence of arguments leads to quantum logic, to an orthomodular lattice, and to the classical Hilbert spaces. However,
this abstract theory does not yet contain Planck’s constant ℏ. We argue, that ℏ can be obtained, if the empty theory is applied to real entities and extended by concepts that are usually considered as
classical notions. Introducing the concepts of localizability and homogeneity we define objects by symmetry groups and systems
of imprimitivity. For elementary systems, the irreducible representations of the Galileo group are projective and determined
only up to a parameter z, which is given by z=m/ℏ, where m is the mass of the particle and ℏ Planck’s constant. We show that ℏ has a meaning within quantum mechanics, irrespective of use the of classical concepts in our derivation. 相似文献
10.
Georges Chevalier 《International Journal of Theoretical Physics》2008,47(1):69-80
The Wigner theorem, in its Uhlhorn’s formulation, states that a bijective transformation of the set of all one-dimensional
linear subspaces of a complex Hilbert space which preserves orthogonality is induced by either a unitary or an antiunitary
operator. There exist in the literature many Wigner-type theorems and the purpose of this paper is to prove in an algebraic
setting a very general Wigner-type theorem for projections (idempotent linear mappings). As corollaries, Wigner-type theorems
for projections in real locally convex spaces, infinite dimensional complex normed spaces and Hilbert spaces are obtained. 相似文献
11.
Andrzej?Oko?ów 《Communications in Mathematical Physics》2009,289(1):335-382
A simple diffeomorphism invariant theory of connections with the non-compact structure group of real numbers is quantized. The theory is defined on a four-dimensional ‘space-time’ by an action resembling closely the
self-dual Plebański action for general relativity. The space of quantum states is constructed by means of projective techniques
by Kijowski [1]. Except for this point the applied quantization procedure is based on Loop Quantum Gravity methods. 相似文献
12.
Joseph Slawny 《Journal of statistical physics》2009,135(4):639-650
Most general self-dual spin 1/2 models in any dimension, with interaction that is translation-invariant in a suitable sense
(‘transitive models’), are determined. In the process of classification of such systems, a class of models which are self-dual
in a particularly strong sense is introduced. 相似文献
13.
We survey the realization of quantum mechanics in quaternionic Hilbert spaces following the methods of Mackey, who examined the complex and real cases exploiting the imprimitivity theorem. We show that there exists a unique unitary skew-adjoint operator which commutes with all the observables. This operator not only plays the role of the imaginary unit in the complex case, but allows a complexification of the Hilbert space by the choice of any quaternionic imaginary unit. Difficulties in the definition of time reversal, however, arise because of the properties of the quaternionic field. The introduction of an extra imaginary unit, commuting with the others, is suggested in order to implement time reversal properly. In the Appendix we give the proof of the imprimitivity theorem, in the quaternionic case, that we use in the paper. 相似文献
14.
15.
Peter Nyman 《International Journal of Theoretical Physics》2010,49(1):1-9
In this paper we continue to study so-called “inverse Born’s rule problem”: to construct a representation of probabilistic
data of any origin by a complex probability amplitude which matches Born’s rule. The corresponding algorithm—quantum-like
representation algorithm (QLRA)—was recently proposed by A. Khrennikov (Found. Phys. 35(10):1655–1693, 2005; Physica E 29:226–236, 2005; Dokl. Akad. Nauk 404(1):33–36, 2005; J. Math. Phys. 46(6):062111–062124, 2005; Europhys. Lett. 69(5):678–684, 2005). Formally QLRA depends on the order of conditioning. For two observables (of any origin, e.g., physical or biological) a and b, b|a- and a|b conditional probabilities produce two representations, say in Hilbert spaces H
b|a
and H
a|b
. In this paper we prove that under “natural assumptions” (which hold, e.g., for quantum observables represented by operators
with nondegenerate spectra) these two representations are unitary equivalent. This result proves the consistency of QLRA. 相似文献
16.
Wendelin Werner 《Pramana》2005,64(5):757-773
It has been observed long ago that many systems from statistical physics behave randomly on macroscopic level at their critical
temperature. In two dimensions, these phenomena have been classified by theoretical physicists thanks to conformal field theory,
that led to the derivation of the exact value of various critical exponents that describe their behavior near the critical
temperature. In the last couple of years, combining ideas of complex analysis and probability theory, mathematicians have
constructed and studied a family of random fractals (called ‘Schramm-Loewner evolutions’ or SLE) that describe the only possible
conformally invariant limits of the interfaces for these models. This gives a concrete construction of these random systems,
puts various predictions on a rigorous footing, and leads to further understanding of their behavior. The goal of this paper
is to survey some of these recent mathematical developments, and to describe a couple of basic underlying ideas. We will also
briefly describe some very recent and ongoing developments relating SLE, Brownian loop soups and conformal field theory. 相似文献
17.
C. J. Isham 《International Journal of Theoretical Physics》1997,36(4):785-814
A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of
consistent sets of history propositions. One possibility is to find a scheme in which a unique set is selected in some way.
However, in this paper the alternative approach is considered in which all consistent sets are kept, leading to a type of
‘many-world-views’ picture of the quantum theory. It is shown that a natural way of handling this situation is to employ the
theory of varying sets (presheafs) on the spaceB of all nontrivial Boolean subalgebras of the orthoalgebraUP of history propositions. This approach automatically includes the feature whereby probabilistic predictions are meaningful
only in the context of a consistent set of history propositions. More strikingly, it leads to a picture in which the ‘truth
values’ or ‘semantic values’ of such contextual predictions are not just two-valued (i.e., true and false) but instead lie
in a larger logical algebra—a Heyting algebra—whose structure is determined by the spaceB of Boolean subalgebras ofUP. This topos-theoretic structure thereby gives a coherent mathematical framework in which to understand the internal logic
of the many-world-views picture that arises naturally in the approach to quantum theory based on the ideas of consistent histories. 相似文献
18.
Chris Heunen 《Foundations of Physics》2012,42(7):856-873
We relate notions of complementarity in three layers of quantum mechanics: (i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices. Taking a more general categorical perspective of which the above are instances, we consider dagger monoidal kernel categories for (ii), so that (i) become (sub)endohomsets and (iii) become subobject lattices. By developing a ‘point-free’ definition of copyability we link (i) commutative von Neumann subalgebras, (ii) classical structures, and (iii) Boolean subalgebras. 相似文献
19.
G Baskaran 《Pramana》2002,58(2):427-437
A few billion years of evolutionary time and the complex process of ‘selection’ has given biology an opportunity to explore
a variety of condensed matter phenomena and situations, some of which have been discovered by humans in the laboratory, that
too only in extreme non-biological conditions such as low temperatures, high purity, high pressure etc., in the last centuries.
Biology, at some level, is a complex and self-regulated condensed matter system compared to the ‘inanimate’ condensed matter
systems such as liquid 4He, liquid water or a piece of graphite. In this article I propose a hypothesis that ‘all basic condensed matter physics phenomena
and notions (already known and ones yet to be discovered) mirror in biology’. I explain this hypothesis by considering the
idea of ‘Bose condensation’ or ‘momentum space order’ and discuss two known example of quantum magnetism encountered in biology.
I also provide some new and rather speculative possibility, from light harvesting in biological photosynthesis, of mesoscopic
excition condensation related phenomena at room temperature. 相似文献
20.
Anatolij Dvurecenskij 《International Journal of Theoretical Physics》1998,37(1):23-29
Using Soler's result, we show that the existenceof at least one finitely additive probability measure onthe system of all orthogonally closed subspaces of Swhich is concentrated on a one-dimensional subspace of E can imply that E is a real,complex, or quaternionic Hilbert space. In addition,using the concept of test spaces of Foulis and Randalland introducing various systems of subspaces of E , we give some characterizations of inner productspaces which imply that E is a real, complex, orquaternionic Hilbert space. 相似文献