scholarly journals Formal solution of the master equation via HPT and deformation theory

2002 ◽  
Vol 14 (6) ◽  
Author(s):  
Johannes Huebschmann ◽  
Jim Stasheff
Keyword(s):  
Master Equation ◽  
Deformation Theory ◽  
Formal Solution

scholarly journals ON THE PERTURBATIVE EQUIVALENCE BETWEEN THE HAMILTONIAN AND LAGRANGIAN QUANTIZATIONS

1996 ◽  
Vol 11 (08) ◽  
pp. 1353-1366 ◽  
Author(s):  
I.A. BATALIN ◽  
I.V. TYUTIN
Keyword(s):  
Master Equation ◽  
Formal Solution ◽  
Quantum Master Equation ◽  
Bv Quantization

The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be perturbatively equivalent to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.

SOLVING MASTER EQUATION FOR CALDEIRA–LEGGETT MODEL BY VIRTUE OF THE THERMO ENTANGLED STATE REPRESENTATION AND THE IWOP TECHNIQUE

2012 ◽  
Vol 26 (14) ◽  
pp. 1250085 ◽  
Author(s):  
QIAN-FAN CHEN ◽  
QIAN YE ◽  
ZHI-HUA LI ◽  
HONG-YI FAN
Keyword(s):  
Master Equation ◽  
Formal Solution ◽  
Quantum Master Equation ◽  
Entangled State ◽  
Iwop Technique ◽  
Entangled State Representation ◽  
State Representation ◽  
Initial State ◽  
Thermo Entangled State Representation ◽  
Thermo Entangled State

In the present work, the exact formal solution of the Caldeira–Leggett quantum master equation for the reduced density matrix of an oscillator is obtained by virtue of the thermo entangled state representation and the technique of integration within an ordered product (IWOP) of operators. Also, the solution for high temperature approximation is derived. When the initial state is a coherent state, it will evolve into a displaced-squeezed chaotic state (a mixed state) which shows that decoherence is involved in the Caldeira–Leggett equation due to the interactions between the system and environment.

Theoretical and experimental research on slip and uplift of the timber-concrete composite beam

BioResources ◽  
2020 ◽  
Vol 15 (3) ◽  
pp. 7079-7099
Author(s):  
Jianying Chen ◽  
Guojing He ◽  
Xiaodong (Alice) Wang ◽  
Jiejun Wang ◽  
Jin Yi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Deformation Theory ◽  
Concrete Slab ◽  
Theoretical Calculations ◽  
Structural Element ◽  
Structural Efficiency ◽  
Theoretical Investigations ◽  
New Type ◽  
Interlayer Slip ◽  
Good Agreement

Timber-concrete composite beams are a new type of structural element that is environmentally friendly. The structural efficiency of this kind of beam highly depends on the stiffness of the interlayer connection. The structural efficiency of the composite was evaluated by experimental and theoretical investigations performed on the relative horizontal slip and vertical uplift along the interlayer between composite’s timber and concrete slab. Differential equations were established based on a theoretical analysis of combination effects of interlayer slip and vertical uplift, by using deformation theory of elastics. Subsequently, the differential equations were solved and the magnitude of uplift force at the interlayer was obtained. It was concluded that the theoretical calculations were in good agreement with the results of experimentation.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

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