共查询到20条相似文献,搜索用时 15 毫秒
1.
Antonio Díaz Miranda 《International Journal of Theoretical Physics》1996,35(10):2139-2168
A geometrical way is described to associate quantum states in the sense of geometric quantization to wave functions in the
quantum mechanical sense for each relativistic elementary particle. Explicit computations are made in a number of cases: Klein-Gordon
and Dirac equations, neutrino and antineutrino Weyl equations, and very general cases of massive and massless particles of
arbitrary spin. In this later case one is led in a canonical way to Penrose wave equations. 相似文献
2.
Consider a compact Kähler manifold endowed with a prequantum bundle. Following the geometric quantization scheme, the associated quantum spaces are the spaces of holomorphic sections of the tensor powers of the prequantum bundle. In this paper we construct an asymptotic representation of the prequantum bundle automorphism group in these quantum spaces. We estimate the characters of these representations under some transversality assumption. The formula obtained generalizes in some sense the Lefschetz fixed point formula for the automorphisms of the prequantum bundle preserving its holomorphic structure. Our results will be applied in two forthcoming papers to the quantum representation of the mapping class group. 相似文献
3.
Leonid Polterovich 《Communications in Mathematical Physics》2014,327(2):481-519
We discuss a quantum counterpart, in the sense of the Berezin–Toeplitz quantization, of certain constraints on Poisson brackets coming from “hard” symplectic geometry. It turns out that they can be interpreted in terms of the quantum noise of observables and their joint measurements in operational quantum mechanics. Our findings include various geometric mechanisms of quantum noise production and a noise-localization uncertainty relation. The methods involve Floer theory and Poisson bracket invariants originated in function theory on symplectic manifolds. 相似文献
4.
Wen-Chao Qiang Hua-Ping Zhang Lei Zhang 《International Journal of Theoretical Physics》2016,55(3):1833-1846
In this paper, we find that the geometric global quantum discord proposed by Xu and the total quantum correlations proposed by Hassan and Joag are identical. Moreover, we work out the analytical formulas of the geometric global quantum discord and geometric quantum discord both for two-qubit X states, respectively. We further illustrate how to use these formulas to deal with a few particular examples. We also compare the results achieved by using three kinds of geometric quantum discords. The geometric quantum discord is verified as a tight lower bound of the geometric global quantum discord for two-qubit X states. 相似文献
5.
Keith C. Hannabuss Varghese Mathai Guo Chuan Thiang 《Letters in Mathematical Physics》2018,108(5):1163-1201
We state and prove a general result establishing that T-duality, or the Connes–Thom isomorphism, simplifies the bulk–boundary correspondence, given by a boundary map in K-theory, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to string theory and to the study of the quantum Hall effect and topological insulators with defects in condensed matter physics. 相似文献
6.
《Physics letters. A》2020,384(16):126330
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to first-order partial differential operators. Therefore, the respective dynamics can be explicitly solved through a flow of points in extensions of the phase space. This generalises the geometric dynamics of a harmonic oscillator in the Fock space. We describe all Hamiltonians which are geometrised (in the above sense) by Gaussian and Airy beams and write down explicit solutions for such systems. 相似文献
7.
Measurement-induced nonlocality 总被引:1,自引:0,他引:1
We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and 2 × n dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication. 相似文献
8.
A.A. Abrikosov Jr. 《Annals of Physics》2005,317(1):24-71
Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional “supertime,” we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schrödinger, the momentum and the coherent states ones. 相似文献
9.
We present an information geometric characterization of Grover’s quantum search algorithm. First, we quantify the notion of quantum distinguishability between parametric density operators by means of the Wigner-Yanase quantum information metric. We then show that the quantum searching problem can be recast in an information geometric framework where Grover’s dynamics is characterized by a geodesic on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover’s algorithm. We also discuss possible deviations from Grover’s algorithm within this quantum information geometric setting. 相似文献
10.
11.
A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov–Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase. 相似文献
12.
Quantum gates, which are the essential building blocks of quantum computers, are very fragile. Thus, to realize robust quantum gates with high fidelity is the ultimate goal of quantum manipulation. Here, we propose a nonadiabatic geometric quantum computation scheme on superconducting circuits to engineer arbitrary quantum gates, which share both the robust merit of geometric phases and the capacity to combine with optimal control technique to further enhance the gate robustness. Specifically, in our proposal, arbitrary geometric single-qubit gates can be realized on a transmon qubit, by a resonant microwave field driving, with both the amplitude and phase of the driving being timedependent. Meanwhile, nontrivial two-qubit geometric gates can be implemented by two capacitively coupled transmon qubits, with one of the transmon qubits’ frequency being modulated to obtain effective resonant coupling between them. Therefore, our scheme provides a promising step towards fault-tolerant solid-state quantum computation. 相似文献
13.
The adiabatic geometric phase is calculated in a coupled two quantum dot system, which is entangled through Förster interaction. This phase is then utilized for implementing basic quantum logic gate operation useful in quantum information processing. Such gates based on geometric phase provide fault-tolerant quantum computing. 相似文献
14.
In anomaly-free quantum field theories the integrand in the bosonic functional integral—the exponential of the effective action
after integrating out fermions—is often defined only up to a phase without an additional choice. We term this choice ``setting
the quantum integrand'. In the low-energy approximation to M-theory the E8-model for the C-field allows us to set the quantum integrand using geometric index theory. We derive mathematical results of independent
interest about pfaffians of Dirac operators in 8k+3 dimensions, both on closed manifolds and manifolds with boundary. These theorems are used to set the quantum integrand
of M-theory for closed manifolds and for compact manifolds with either temporal (global) or spatial (local) boundary conditions.
In particular, we show that M-theory makes sense on arbitrary 11-manifolds with spatial boundary, generalizing the construction
of heterotic M-theory on cylinders.
The work of D.F. is supported in part by NSF grant DMS-0305505. The work of G.M. is supported in part by DOE grant DE-FG02-96ER40949 相似文献
15.
A scheme to perfectly preserve an initial qubit state in
geometric quantum computation is proposed for a single-qubit geometric
quantum gate in a nuclear magnetic resonance system. At first, by
adjusting some magnetic field parameters, one can let the dynamic
phase be proportional to the geometric phase. Then, by controlling
the azimuthal angle in the initial state, we may realize a
geometric quantum gate whose fidelity is equal to one under
cyclic evolution. This means that the quantum information is no
distortion in the process of geometric quantum computation. 相似文献
16.
17.
Majorana's stellar representation provides an intuitive picture in which quantum states in high-dimensional Hilbert space can be observed using the trajectory of Majorana stars. We consider the Majorana's stellar representation of the quantum geometric tensor for a spin state up to spin-3/2. The real and imaginary parts of the quantum geometric tensor, corresponding to the quantum metric tensor and Berry curvature, are therefore obtained in terms of the Majorana stars. Moreover, we work out the expressions of quantum geometric tensor for arbitrary spin in some important cases. Our results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana's stars. 相似文献
18.
19.
Eduard Prugovečki 《Foundations of Physics》1996,26(12):1645-1668
The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed. 相似文献
20.
This paper develops a new complex Hamiltonian structure forn-soliton solutions for a class of integrable equations such as the nonlinear Schrödinger, sine-Gordon and Korteweg-de Vries hierarchies of equations that yields, amongst other things, geometric phases in the sense of Hannay and Berry. For example, one of the possible soliton geometric phases is manifested by the well known phase shift that occurs for interacting solitons. The main new tools are complex angle representations that linearize the corresponding Hamiltonian flows on associated noncompact Jacobi varieties. This new structure is obtained by taking appropriate limits of the differential equations describing the class of quasi-periodic solutions. A method of asymptotic reduction of the angle representations is introduced for investigating soliton geometric phases that are related to the presence of monodromy at singularities in the space of parameters. In particular, the phase shift of interacting solitons can be expressed as an integral over a cycle on an associated Riemann surface. In this setting, soliton geometric asymptotics are constructed for studying geometric phases in the quantum case. The general approach is worked out in detail for the three specific hierarchies of equations mentioned. Some links with -functions, the braid group and geometric quantization are pointed out as well.Communicated by A. Jaffe 相似文献