Add time-dependent example

examples/sbm_laser_pulse.jl

@@ -0,0 +1,98 @@
+#=
+    Example of a time-dependent Hamitloninan on a zero-temperature Spin-Boson Model with an hard cut-off Ohmic spectral density J(ω) = 2αω when ω < ωc and 0 otherwise
+
+    The dynamics is simulated using the T-TEDOPA method that maps the normal modes environment into a non-uniform tight-binding chain.
+
+    H = \\frac{ω_0}{2} σ_z + Δ σ_x + σ_x ϵ sin(ωdrive t) + c_0 σ_x(b_0^\\dagger + b_0) + \\sum_{i=0}^{N-1} t_i (b_{i+1}^\\dagger b_i +h.c.) + \\sum_{i=0}^{N-1} ϵ_i b_i^\\dagger b_i  
+=#
+
+using MPSDynamics, Plots, LaTeXStrings
+
+import MPSDynamics: disp
+
+#----------------------------
+# Physical parameters
+#----------------------------
+
+d = 4 # number of Fock states of the chain modes
+
+N = 60 # length of the chain
+
+α = 0.005 # coupling strength
+
+Δ = 0.0 # tunneling 
+
+ω0 = 0.8 # TLS gap
+
+s = 1 # ohmicity
+
+cpars = chaincoeffs_ohmic(N, α, s) # chain parameters, i.e. on-site energies ϵ_i, hopping energies t_i, and system-chain coupling c_0
+
+Trabi = 30.0 # Rabi period of the drive
+
+ϵ = 2*pi / Trabi # Intensity of the drive
+
+ωdrive = ω0 # Frequency of the drive
+
+Ndrive = 1 #Number of the site on which the drive is applied
+#-----------------------
+# Simulation parameters
+#-----------------------
+
+dt = 0.5 # time step
+
+tfinal = 100.0 # simulation time
+
+method = :TDVP1 # time-evolution method
+
+D = [6] # MPS bond dimension
+
+#---------------------------
+# MPO and initial state MPS
+#---------------------------
+
+numsteps = length(collect(0:dt:tfinal))-1
+timelist = [(i-1)*dt for i=1:numsteps+1]
+
+Ht = [ϵ*sx*sin(ωdrive*tstep) for tstep in timelist] # Time dependent Hamiltonian term MPO
+
+H = spinbosonmpo(ω0, Δ, d, N, cpars) # MPO representation of the Hamiltonian
+
+ψ = unitcol(2,2) # Initial low-z system state 
+
+A = productstatemps(physdims(H), state=[ψ, fill(unitcol(1,d), N)...]) # MPS representation of |ψ>|Vacuum>
+
+#---------------------------
+# Definition of observables
+#---------------------------
+
+ob1 = OneSiteObservable("sz", sz, 1)
+
+ob2 = OneSiteObservable("chain mode occupation", numb(d), (2,N+1))
+
+ob3 = TwoSiteObservable("SXdisp", sx, disp(d), [1], collect(2:N+1))
+
+#-------------
+# Simulation
+#------------
+
+A, dat = runsim(dt, tfinal, A, H;
+                name = "Driving field on ohmic spin boson model",
+                method = method,
+                obs = [ob1],
+                convobs = [ob1],
+                params = @LogParams(N, d, α, Δ, ω0, s),
+                convparams = D,
+                timedep = true,
+                Ndrive = Ndrive,
+                Htime = Ht,
+                verbose = false,
+                save = true,
+                plot = true,
+                );
+
+#----------
+# Plots
+#----------
+
+plot(dat["data/times"], dat["data/sz"], label=["Dmax = $D"], xlabel=L"t",ylabel=L"\sigma_z", title="")

src/run_1TDVP.jl

@@ -1,5 +1,6 @@
-function run_1TDVP(dt, tmax, A, H, Dmax; obs=[], timed=false, reduceddensity=false, kwargs...)
+function run_1TDVP(dt, tmax, A, H, Dmax; obs=[], timed=false, reduceddensity=false, timedep=false, kwargs...)
     A0=deepcopy(A)
+    H0=deepcopy(H)
     data = Dict{String,Any}()
 
     numsteps = length(collect(0:dt:tmax))-1
@@ -23,13 +24,18 @@ function run_1TDVP(dt, tmax, A, H, Dmax; obs=[], timed=false, reduceddensity=fal
     for tstep=1:numsteps
         @printf("%i/%i, t = %.3f ", tstep, numsteps, times[tstep])
         println()
+        if timedep
+	   Ndrive = kwargs[:Ndrive]
+	   Htime = kwargs[:Htime]
+           H0[Ndrive][1,1,:,:] = H[Ndrive][1,1,:,:] + Htime[tstep][:,:]
+        end
         if timed
-            val, t, bytes, gctime, memallocs = @timed tdvp1sweep!(dt, A0, H, F; kwargs...)
+            val, t, bytes, gctime, memallocs = @timed tdvp1sweep!(dt, A0, H0, F; kwargs...)
             println("\t","ΔT = ", t)
             A0, F = val
             ttdvp[tstep] = t
         else
-            A0, F = tdvp1sweep!(dt, A0, H, F; kwargs...)
+            A0, F = tdvp1sweep!(dt, A0, H0, F; kwargs...)
         end
         exp = measure(A0, obs; t=times[tstep])
         for (i, ob) in enumerate(obs)