Time development of quantum lattice systems

The time development of quantum lattice systems is studied with a weaker assumption on the growth of the potential than has been considered previously.Battelle Fellow.     

Time evolution of quantum fractals

We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.     

Time evolution of a quantum mechanical maser model

The time evolution of the Dicke maser model describing N spins ($\text{s =}\text{1}\text{2}$) interacting by a dipole coupling with one mode of an electromagnetic field, is studied for finite N. The mean photon number and its mean square deviation can be calculated as functions of time for various initial states. For not too large times, these quantities show a periodic behavior given by elliptic functions.     

Time operator and quantum projection evolution

In this paper, we consider time as a dynamical variable. In particular, we present the explicit realization of the time operator within four-dimensional nonrelativistic spacetime. The approach assumes including events as a part of the evolution. The evolution is not driven by the physical time, but it is based on the causally related physical events. The usual Schrödinger unitary evolution can be easily derived as a special case of the three-dimensional projection onto the space of simultaneous events. Also the time—energy uncertainty relation makes clear and mathematically rigorous interpretation.     

On averaging of time evolution of quantum spin lattice systems

An investigation of a procedure of obtaining irreversible dynamics for systems in contact with surroundings is given.Research supported by M. Skodowska-Curie Fund Grant No. 0IP74-01416.     

Time evolution for quantum systems at finite temperature

This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation is non-perturbative and fully quantized. Various numerical methods used to compute the needed path integrals in complex time were tested and their effectiveness was compared. For checking the formalism we used the harmonic oscillator where the numerical results could be compared with exact solutions. Interesting results were also obtained for a system that presents tunneling. A ring of coupled oscillators was treated in order to try to check self-consistency in the thermodynamic limit. The short time distribution seems to propagate causally in the relativistic case. Our formalism can be extended easily to field theories where it remains to be seen if relevant models will be computable.     

Time evolution and spectral concentration in quantum systems

Time dependence and spectral concentration in quantum systems are reviewed. A partitioning technique is presented based on retarded and advanced propagators. The associated fundamental time symmetry is conveniently formulated in correspondence with the classical notion of reversal of time and momenta. Symmetry breakings occur when a particular convolution product is broken up into past and future times.The separation of the time variable into two scales is discussed. Comparison with the wave and reaction operator formulation gives a reciprocal relationship between these times together with an emphasis of the role played by the associated spectral density. Examples are given from applications of Weyl's complex eigenvalue theory.     

Euclidean quantum gravity on a lattice

We construct a number of related euclidean lattice formulations of quantum gravity. The first version incorporates a path integral over discrete manifolds built out of four-cubes embedded in a higher dimensional flat hypercubic lattice. We show this expression is equal to a corresponding path integral in a local lattice field theory. The field theoretic path integral diverges and lacks a satisfactory vacuum state. This divergence can be interpreted as a consequence of a divergent phase space available for topological fluctuations in the four-manifolds of the original path integral. A modified version of the path integral over manifolds converges. We construct a Schrödinger equation and hamiltonian for the modified theory. The hamiltonian is self-adjoint, but as a result of the large phase space available for topological fluctuations, the hamiltonian's spectrum is probably not bounded from below. We show briefly how the flat enveloping space—time can be removed from most of the theories we present and how matter fields can be included.     

A lattice of electromagnetic solitons in a superlattice formed by a system of quantum dots

Considering the Maxwell equations for the electromagnetic-field propagation in a solid with a three-dimensional superlattice of quantum dots linked by strong tunneling along one axis, we obtained a phenomenological equation in the form of the classical 2+1-dimensional sine-Gordon equation. Electrons were considered classically in the formalism of the Boltzmann kinetic equation for the distribution function. Solutions were obtained as a soliton lattice for the vector potential of the electric field. These lattices emerge as a consequence of the coherent change of the classical distribution function and the electric field generated by tunneling electrons in a system of quantum wells.     

Time evolution of non-Hermitian quantum systems and generalized master equations

We inquire into the time evolution of quantum systems associated with pseudo-or quasi-Hermitian Hamiltonians. We obtain, in the pseudo-Hermitian case, a generalized Liouville-von Neumann equation for closed systems. We show that quantum systems with quasi-Hermitian Hamiltonians admit the proper interpretation in terms of open quantum system and derive a generalized Lindblad-Kossakowski equation. Finally, we extend such formalism to the study of decaying systems. Partially supported by PRIN “Sintesi”.     

Entanglement evolution of a two-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a two-qubit system under a quantum spin environment at finite temperature in the thermodynamics limit. For the case under study, we find different initial states will result in different entanglement evolution, what deserves mentioning here is that the state |Ψ=cosα|01+sinα|10 is most robust than other states when π/2<α<π, since the entanglement remains unchanged or increased under the spin environment. In addition, we also find the anisotropy parameter Δ can suppress the destruction of decoherence induced by the environment, and the undesirable entanglement sudden death arising from the process of entanglement evolution can be efficiently controlled by the inhomogeneous magnetic field ζ.     

Gibbs states of a one dimensional quantum lattice

A one dimensional infinite quantum spin lattice with a finite range interaction is studied. The Gibbs state in the infinite volume limit is shown to exist as a primary state of a UHF algebra. The expectation value of any local observables in the state as well as the mean free energy depend analytically on the potential, showing no phase transition. The Gibbs state is an extremal KMS state.On leave from Research Institute for Mathematical Sciences, Kyoto University Kyoto, Japan.     

Time evolution of infinite one-dimensional Coulomb system

We consider one-dimensional Coulomb systems and their time evolution given by the Newton law. We give existence and uniqueness theorems for the solutions of the equations governing the systems in the thermodynamic limits.Partially supported by the Italian C.N.R. and by the I.H.E.S.     

Crystal lattice quantum computer

31 P nucleus can be used to represent a quantum bit (‘qubit’) with a relatively long relaxation time. In a CeP crystal lattice, ³¹P nuclei are periodically situated in three dimensions at distances of about 6 Å. The application of a static magnetic field gradient in one direction causes differences in the Zeemanfrequencies of separate nuclei. This allows thousands of distinct qubits to be individually addressed. Initializations of the qubits can be done efficiently by the Pound–Overhauser double resonance effect on the nuclear spins and the antiferromagnetically ordered 4f electron spins of cerium ions. Logic operations can be performed by simple pulse sequences, and computational results after logic operations can be measured by the nuclear magnetic resonance of neighboring nuclei, or the electron resonance of neighboring 4f electrons of cerium ions. Received: 26 October 1998/Accepted: 29 October 1998     

Perturbation of the evolution of a quantum system induced by its environment

We consider the effects of a massive homogeneous body on the state vector of a molecule passing nearby. The interchange of virtual photons between body and molecule cause the latter to fail a proposed criterion of isolation even for molecules consisting of as little as 10⁴ particles. The calculation contains no free parameters but furnishes only a lower bound to the effects. The fact that matter consists of electrically charged particles is essential for a smooth transition from the quantum to the classical behavior as the system grows larger.     

On the mixing-enhancing dynamical maps and mixing-enhancing evolution of a quantum system

The mixing-enhancing (in the sense of Uhlmann) dynamical maps and dynamical evolution is studied. We give a necessary and sufficient condition for a dynamical map (and dynamical evolution) of a quantum system to be mixing-enhancing. In the case of a finite- dimensional Hilbert space this condition is equivalent to the condition that the dynamical map (dynamical evolution) preserve the most mixed state and the von Neumann entropy be non- decreasing. It is proved that, in contrast with the finite-dimensional case, increasing of the von Neumann entropy under a dynamical map (for any initial state) does not imply that the dynamical map is mixing-enhancing. We also give a necessary and sufficient condition for an infinitesimal generator of a norm-continuous dynamical semigroup to be mixing-enhancing.     

Orthogonality catastrophe and the speed of quantum evolution in a qubit-spin-bath system

The orthogonality catastrophe (OC) of quantum many-body systems is an important phenomenon in condensed matter physics. Recently, an interesting relationship between the OC and the quantum speed limit (QSL) was shown (Fogarty 2020 Phys. Rev. Lett. 124 110601). Inspired by the remarkable feature, we provide a quantitative version of the quantum average speed as another different method to investigate the measure of how it is close to the OC dynamics. We analyze the properties of an impurity qubit embedded into an isotropic Lipkin-Meshkov-Glick spin model, and show that the OC dynamics can also be characterized by the average speed of the evolution state. Furthermore, a similar behavior of the actual speed of quantum evolution and the theoretical maximal rate is shown which can provide an alternative speed-up protocol allowing us to understand some universal properties characterized by the QSL.