Difference between revisions of "Thermalize.m"

From Spinach Documentation Wiki
Jump to: navigation, search
(Sync syntax/arguments/outputs with current Spinach source)
(Update function See also links and function index membership)
 
(7 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
{{DISPLAYTITLE:thermalize.m}} __NOTOC__
 
{{DISPLAYTITLE:thermalize.m}} __NOTOC__
−
 
+
Modifies the relaxation superoperator to drive the system to the user-specified target state using the inhomogeneous master equation formalism, or to the equilibrium state of the lab-frame Hamiltonian at the temperature provided by the user using the DiBari-Levitt formalism.
−
Modifies a symmetric relaxation superoperator to relax the system towards a user-specified state using the Levante-Ernst method ( https://doi.org/10.1016/0009-2614(95)00578-R ) which works by adding one-way cross-relaxation with the unit state.
 
  
 
==Syntax==
 
==Syntax==
  
−
R=thermalize(spin_system,R,HLSPS,T,rho_eq,method)
 
−
 
−
==Arguments==
 
−
 
−
R      - symmetric negative definite relaxation super-
 
−
              operator that drives the system towards the
 
−
              zero state vector; this may be obtained from
 
−
              relaxation.m if inter.equilibrium is 'zero'
 
  
−
     HLSPS   - lab frame Hamiltonian left side product super-
+
     R=thermalize(spin_system,R,HLSPS,T,rho_eq,method)
−
              operator, available from hamiltonian.m (also
 
−
              call orientation.m if necessary); this is not
 
−
              required for IME formalism (pass empty array)
 
  
−
    T      - absolute temperature, not required for the
+
==Parameters==
−
              IME formalism (pass empty array)
 
  
−
    rho_eq  - thermal equilibrium state, not required for
 
−
              the DiBari-Levitt formalism (pass empty array)
 
  
−
    method  - 'dibari' for DiBari-Levitt thermalisation,
+
  R      - symmetric negative definite relaxation superoperator that
−
              'IME' for the inhomogeneous master equation
+
            drives the system towards the zero state vector; this may
 +
            be obtained from relaxation.m if inter.equilibrium is 'zero'
 +
 +
  HLSPS  - lab-frame Hamiltonian left side product superoperator,
 +
            available from hamiltonian.m; also call orientation.m if
 +
            necessary. This is not required for IME formalism, pass []
 +
 +
  T      - absolute temperature, not required for IME formalism,
 +
            pass []
 +
 +
  rho_eq  - thermal equilibrium state, not required for DiBari-Levitt
 +
            formalism, pass []
 +
 +
  method  - 'dibari' for DiBari-Levitt thermalisation, 'IME' for the
 +
            inhomogeneous master equation
  
 
==Outputs==
 
==Outputs==
  
−
R      - thermalized relaxation superoperator
 
  
−
Note: to work correctly, IME requires the population of the unit state
+
  R      - thermalised relaxation superoperator
−
      in the state vector to be exactly 1. Spinach has no way of check-
 
−
      ing or enforcing this requirement - take due care.
 
−
 
 
−
Note: DiBari-Levitt method is computationally expensive, but tends to
 
−
      work better than IME, particularly in exotic regimes.
 
−
 
 
−
ilya.kuprov@weizmann.ac.il
 
−
fije@inano.au.dk
 
  
 
==Notes==
 
==Notes==
  
−
Liouville space spherical tensor formalism only.
+
IME requires the population of the unit state in the state vector to be exactly 1; Spinach cannot check or enforce this requirement. DiBari-Levitt thermalisation is computationally expensive, but tends to work better than IME, particularly in exotic regimes.
  
 
==See also==
 
==See also==
−
 
+
[[magpump.m]], [[relaxation.m]], [[kinetics.m]], [[lindbladian.m]], [[basis.m]], [[create.m]], [[reduce.m]], [[Kernel_functions]]
−
[[magpump.m]], [[relaxation.m]], [[kinetics.m]], [[lindbladian.m]]
 
−
 
 
  
 
''Version 2.2, authors: [[Ilya Kuprov]]''
 
''Version 2.2, authors: [[Ilya Kuprov]]''

Latest revision as of 19:42, 6 June 2026

Modifies the relaxation superoperator to drive the system to the user-specified target state using the inhomogeneous master equation formalism, or to the equilibrium state of the lab-frame Hamiltonian at the temperature provided by the user using the DiBari-Levitt formalism.

Syntax

    R=thermalize(spin_system,R,HLSPS,T,rho_eq,method)

Parameters

  R       - symmetric negative definite relaxation superoperator that
            drives the system towards the zero state vector; this may
            be obtained from relaxation.m if inter.equilibrium is 'zero'

  HLSPS   - lab-frame Hamiltonian left side product superoperator,
            available from hamiltonian.m; also call orientation.m if
            necessary. This is not required for IME formalism, pass []

  T       - absolute temperature, not required for IME formalism,
            pass []

  rho_eq  - thermal equilibrium state, not required for DiBari-Levitt
            formalism, pass []

  method  - 'dibari' for DiBari-Levitt thermalisation, 'IME' for the
            inhomogeneous master equation

Outputs

  R       - thermalised relaxation superoperator

Notes

IME requires the population of the unit state in the state vector to be exactly 1; Spinach cannot check or enforce this requirement. DiBari-Levitt thermalisation is computationally expensive, but tends to work better than IME, particularly in exotic regimes.

See also

magpump.m, relaxation.m, kinetics.m, lindbladian.m, basis.m, create.m, reduce.m, Kernel_functions

Version 2.2, authors: Ilya Kuprov

Retrieved from "https://spindynamics.org/wiki/index.php?title=Thermalize.m&oldid=9572"