Solution of the eigenvalue problem of a N-level system coupled to a bosonic degree of freedom without using RWA

1987 ◽  
Vol 20 (5) ◽  
pp. 1155-1172 ◽  
Author(s):  
N Klenner ◽  
J Weis
Keyword(s):  
Eigenvalue Problem ◽  
Degree Of Freedom ◽  
Level System ◽  
N Level

Determination of the first n modes of a tall building from a reduced eigenvalue problem

1964 ◽  
Vol 54 (4) ◽  
pp. 1233-1254
Author(s):  
Moshe F. Rubinstein
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Tall Building ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Story Building

Abstract The first n natural frequencies and mode shapes of an N degree of freedom structure (n < N) are derived from the solution of a reduced eigenvalue problem of order smaller than N. The reduced eigenvalue problem is formulated by using experience to select approximations to the first n modes desired. Accuracy is improved when more than n modes are selected. The method is illustrated by a study on an 18 story building.

scholarly journals Intuitionistic Quantum Logic of an n-level System

2009 ◽  
Vol 39 (7) ◽  
pp. 731-759 ◽  
Author(s):  
Martijn Caspers ◽  
Chris Heunen ◽  
Nicolaas P. Landsman ◽  
Bas Spitters
Keyword(s):  
Quantum Logic ◽  
Level System ◽  
N Level

scholarly journals REDUCED DYNAMICS FROM THE UNITARY GROUP TO SOME FLAG MANIFOLDS: INTERACTING MATRIX RICCATI EQUATIONS

2009 ◽  
Vol 06 (04) ◽  
pp. 573-581 ◽  
Author(s):  
KAZUYUKI FUJII ◽  
HIROSHI OIKE
Keyword(s):  
Differential Equations ◽  
Riccati Equation ◽  
Time Evolution ◽  
Unitary Group ◽  
Natural Generalization ◽  
Flag Manifolds ◽  
Level System ◽  
Nonlinear Superposition ◽  
N Level ◽  
Nonlinear Superposition Formula

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper Chaturvedi et al. [1] (arXiv: 0706.0964 [quant-ph]).

scholarly journals Controllable dynamics of a dissipative two-level system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wei Wu ◽  
Ze-Zhou Zhang
Keyword(s):  
Decay Rate ◽  
Degree Of Freedom ◽  
Level System ◽  
Dissipative Dynamics

AbstractWe propose a strategy to modulate the decoherence dynamics of a two-level system, which interacts with a dissipative bosonic environment, by introducing an ancillary degree of freedom. It is revealed that the decay rate of the two-level system can be significantly suppressed under suitable steers of the assisted degree of freedom. Our result provides an alternative way to fight against decoherence and realize a controllable quantum dissipative dynamics.

scholarly journals Quality-Factor Enhancing Locations for Substrate Mounted Resonators

2020 ◽  
Vol 25 (3) ◽  
pp. 318-326
Author(s):  
Allen Anilkumar ◽  
Arun George ◽  
Gireesh Sharma N.
Keyword(s):  
Eigenvalue Problem ◽  
Quality Factor ◽  
Characteristic Equation ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Structural Interaction ◽  
Single Degree ◽  
Lookup Tables

An important but often overlooked factor that affects the performance of a meso/micro electro mechanical vibratory sensor is the structural interaction between the sensor's resonator and the substrate on which it is mounted. Situating resonators at node points eliminates this interaction and thereby helps to improve a resonator's quality-factor for a particular mode of vibration. This paper addresses the problem of locating a single degree of freedom spring-mass resonator on a generic cantilever substrate. The loci of natural frequencies obtained when the resonator's mounting location is varied are developed, and the nodal locations are identified. Thereafter a method to obtain these locations from the characteristic equation without solving the associated eigenvalue problem is described. Lookup tables detailing the nodal locations and the corresponding natural frequencies for various resonator parameters are presented. It is found that at these special nodal locations, the magnitude of the power transmitted through anchors is negligible, which ensures minimal structural interaction between the resonator and the substrate.

On entanglement distillation and quantum error correction for unknown states and channels

Open Physics ◽  
2003 ◽  
Vol 1 (4) ◽  
Author(s):  
Pawel Horodecki
Keyword(s):  
Quantum State ◽  
Transmission Rate ◽  
Single Copy ◽  
Quantum Error Correction ◽  
Quantum Channels ◽  
Level System ◽  
Open Problems ◽  
Single Qubit ◽  
N Level ◽  
Quantum Error

AbstractWe consider the problem of invariance of distillable entanglement D and quantum capacities Q under erasure of information about single copy of quantum state or channel respectively. We argue that any 2 ⊗N two-way distillable state is still two-way distillable after erasure of single copy information. For some known distillation protocols the obtained two-way distillation rate is the same as if Alice and Bob knew the state from the very beginning. The isomorphism between quantum states and quantum channels is also investigated. In particular it is pointed out that any transmission rate down the channel is equal to distillation rate with formal LOCC-like superoperator that uses in general nonphysical Alice actions. This allows to we prove that if given channel Λ has nonzero capacity (Q → or Q ⟺) then the corresponding quantum state ϱ(Λ) has nonzero distillable entanglement (D → or D ⟺). Follwoing the latter arguments are provided that any channel mapping single qubit into N level system allows for reliable two-way transmission after erasure of information about single copy. Some open problems are discussed.

Sign in / Sign up

Export Citation Format

Share Document