From a6570c39f48ea8c664e307958c72bd3db54d0dae Mon Sep 17 00:00:00 2001
From: Anton Akhmerov <anton.akhmerov@gmail.com>
Date: Fri, 23 Aug 2013 10:01:03 +0200
Subject: [PATCH] update noise: allow to use reflection, disallow Green's
functions
---
kwant/physics/noise.py | 27 +++++++++++++++++----------
kwant/physics/tests/test_noise.py | 31 +++++++------------------------
2 files changed, 24 insertions(+), 34 deletions(-)
diff --git a/kwant/physics/noise.py b/kwant/physics/noise.py
index 6a787806..92b9a9cb 100644
--- a/kwant/physics/noise.py
+++ b/kwant/physics/noise.py
@@ -10,20 +10,27 @@ import numpy as np
def two_terminal_shotnoise(smatrix):
"""Compute the shot-noise in a two-terminal setup.
- [Given by tr((1 - t*t^\dagger) * t*t^\dagger)]."""
+
+ In a two terminal system the shot noise is given by `tr((1 - t*t^\dagger) *
+ t*t^\dagger)`.
+
+ Parameters
+ ----------
+ smatrix : `~kwant.solvers.common.BlockResult` instance
+ A two terminal scattering matrix.
+
+ Returns
+ -------
+ noise : float
+ Shot noise measured in noise quanta `2 e^3 |V| / pi hbar`.
+ """
if len(smatrix.lead_info) != 2:
raise ValueError("Only works for two-terminal systems!")
- if 1 in smatrix.out_leads and 0 in smatrix.in_leads:
- ttdag = smatrix._a_ttdagger_a_inv(1, 0)
- if 0 in smatrix.out_leads and 1 in smatrix.in_leads:
- ttdag = smatrix._a_ttdagger_a_inv(0, 1)
- else:
- raise ValueError("Need S-matrix block for transmission!")
-
- ttdag -= np.dot(ttdag, ttdag)
- return np.trace(ttdag).real
+ t = smatrix.submatrix(smatrix.out_leads[0], smatrix.in_leads[0])
+ ttdag = np.dot(t, t.conj().T)
+ return np.trace(ttdag - np.dot(ttdag, ttdag)).real
# A general multi-terminal routine for noise would need to also have the
diff --git a/kwant/physics/tests/test_noise.py b/kwant/physics/tests/test_noise.py
index 0bf2a5c2..adc71d78 100644
--- a/kwant/physics/tests/test_noise.py
+++ b/kwant/physics/tests/test_noise.py
@@ -15,7 +15,7 @@ from kwant.physics.noise import two_terminal_shotnoise
n = 5
chain = kwant.lattice.chain()
-def _twoterminal_system():
+def twoterminal_system():
np.random.seed(11)
system = kwant.Builder()
lead = kwant.Builder(kwant.TranslationalSymmetry((1,)))
@@ -28,30 +28,22 @@ def _twoterminal_system():
lead[chain(0), chain(1)] = t
system.attach_lead(lead)
system.attach_lead(lead.reversed())
- return system.finalized()
+ return system
-def test_twoterminal_input():
+def test_multiterminal_input():
"""Input checks for two_terminal_shotnoise"""
- fsys = _twoterminal_system()
- sol = kwant.solve(fsys, out_leads=[0], in_leads=[0])
+ sys = twoterminal_system()
+ sys.attach_lead(sys.leads[0].builder)
+ sol = kwant.solve(sys.finalized(), out_leads=[0], in_leads=[0])
assert_raises(ValueError, two_terminal_shotnoise, sol)
-class LeadWithOnlySelfEnergy(object):
- def __init__(self, lead):
- self.lead = lead
-
- def selfenergy(self, energy, args=()):
- assert args == ()
- return self.lead.selfenergy(energy)
-
-
def test_twoterminal():
"""Shot noise in a two-terminal conductor"""
- fsys = _twoterminal_system()
+ fsys = twoterminal_system().finalized()
sol = kwant.solve(fsys)
t = sol.submatrix(1, 0)
@@ -59,12 +51,3 @@ def test_twoterminal():
noise_should_be = np.sum(Tn * (1 - Tn))
assert_almost_equal(noise_should_be, two_terminal_shotnoise(sol))
-
- # replace leads successively with self-energy
- fsys.leads[0] = LeadWithOnlySelfEnergy(fsys.leads[0])
- sol = kwant.solve(fsys)
- assert_almost_equal(noise_should_be, two_terminal_shotnoise(sol))
-
- fsys.leads[1] = LeadWithOnlySelfEnergy(fsys.leads[1])
- sol = kwant.solve(fsys)
- assert_almost_equal(noise_should_be, two_terminal_shotnoise(sol))
--
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