View Full Version : Decoherence question
Mike Stay
Dec10-04, 10:18 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nIn general, quantum systems don\'t decohere into mixtures of energy\neigenstates. Sometimes it\'s position eigenstates, sometimes some\nother basis. I\'ve heard the term "master equation" used in connection\nwith determining which is the preferred basis for a given system. Can\nsomeone explain what one is, and how it works?\n\nThanks,\nMike\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In general, quantum systems don't decohere into mixtures of energy
eigenstates. Sometimes it's position eigenstates, sometimes some
other basis. I've heard the term "master equation" used in connection
with determining which is the preferred basis for a given system. Can
someone explain what one is, and how it works?
Thanks,
Mike
Arnold Neumaier
Dec20-04, 10:05 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Mike Stay wrote:\n> In general, quantum systems don\'t decohere into mixtures of energy\n> eigenstates. Sometimes it\'s position eigenstates, sometimes some\n> other basis. I\'ve heard the term "master equation" used in connection\n> with determining which is the preferred basis for a given system. Can\n> someone explain what one is, and how it works?\n\nA quantum master equation is a dynamical equation for the density matrix\nof a dissipative quantum systems, which approximates a quantum system\nweakly coupled to an environment at time scales long compared to the\ntypical interaction time but short enough to avoid recurrence effects.\nMore precisely, the dynamics is given by a completely positive Markovian\nsemigroup in a representation named after Lindblad, wo discovered its\ngeneral form.\n\nFor a classical damped linear system xdot(t)=Ax(t) with a matrix A whose\nspectrum is in the left complex half plane, the contribution of x in the\ninvariant subspace corresponding to eigenvalues which are not purely\nimaginary decays to zero, so that at large times t, x(t) essentially\napproaches the invariant subspace corresponding to purely imaginary\neigenvalues.\n\nFor a quantum master equation, a similar analysis holds and shows that\n(under suitable conditions) the density matrix at times much larger than\nthe so-called decoherence time approaches a block diagonal form in a\nsuitable basis. Thus it (almost) commutes with a special set of\nobservables, which define the \'pointer variables\' of the system. These\npointer variables therefore behave essentially classically. If the\npointer variables form a complete set of commuting variables, the\ndensity matrix approaches a diagonal matrix, and the basis in which this\nhappens is called the \'preferred basis\'.\n\nFor details, see, e.g., cond-mat/0011204 or gr-qc/9406054\n\n\nArnold Neumaier\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Mike Stay wrote:
> In general, quantum systems don't decohere into mixtures of energy
> eigenstates. Sometimes it's position eigenstates, sometimes some
> other basis. I've heard the term "master equation" used in connection
> with determining which is the preferred basis for a given system. Can
> someone explain what one is, and how it works?
A quantum master equation is a dynamical equation for the density matrix
of a dissipative quantum systems, which approximates a quantum system
weakly coupled to an environment at time scales long compared to the
typical interaction time but short enough to avoid recurrence effects.
More precisely, the dynamics is given by a completely positive Markovian
semigroup in a representation named after Lindblad, wo discovered its
general form.
For a classical damped linear system xdot(t)=Ax(t) with a matrix A whose
spectrum is in the left complex half plane, the contribution of x in the
invariant subspace corresponding to eigenvalues which are not purely
imaginary decays to zero, so that at large times t, x(t) essentially
approaches the invariant subspace corresponding to purely imaginary
eigenvalues.
For a quantum master equation, a similar analysis holds and shows that
(under suitable conditions) the density matrix at times much larger than
the so-called decoherence time approaches a block diagonal form in a
suitable basis. Thus it (almost) commutes with a special set of
observables, which define the 'pointer variables' of the system. These
pointer variables therefore behave essentially classically. If the
pointer variables form a complete set of commuting variables, the
density matrix approaches a diagonal matrix, and the basis in which this
happens is called the 'preferred basis'.
For details, see, e.g., http://www.arxiv.org/abs/cond-mat/0011204 or http://www.arxiv.org/abs/gr-qc/9406054
Arnold Neumaier
Kwok Man Hui
Dec24-04, 06:49 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Mon, 20 Dec 2004, Arnold Neumaier wrote:\n\n> Mike Stay wrote:\n>> In general, quantum systems don\'t decohere into mixtures of energy\n>> eigenstates. Sometimes it\'s position eigenstates, sometimes some\n>> other basis. I\'ve heard the term "master equation" used in connection\n>> with determining which is the preferred basis for a given system. Can\n>> someone explain what one is, and how it works?\n>\n> A quantum master equation is a dynamical equation for the density matrix\n> of a dissipative quantum systems, which approximates a quantum system\n> weakly coupled to an environment at time scales long compared to the\n> typical interaction time but short enough to avoid recurrence effects.\n> More precisely, the dynamics is given by a completely positive Markovian\n> semigroup in a representation named after Lindblad, wo discovered its\n> general form.\n>\n> For details, see, e.g., cond-mat/0011204 or gr-qc/9406054\n\nAbstract from cond-mat/0011204:\n\nA central problem in the theory of the dynamics of open quantum systems is\nthe derivation of a rigorous and computationally tractable master equation\nfor the reduced system density matrix. Most generally, the evolution of an\nopen quantum system is described by a completely positive linear map. We\nshow how to derive a completely positive Markovian master equation (the\nLindblad equation) from such a map by a coarse graining procedure. We\nprovide a novel and explicit recipe for calculating the coefficients of\nthe master equation, using perturbation theory in the weak-coupling limit.\nThe only parameter external to our theory is the coarse-graining\ntime-scale. We illustrate the method by explicitly deriving the master\nequation for the spin-boson model. The results are evaluated for the\nexactly solvable case of pure dephasing, and an excellent agreement is\nfound within the timescale where the Markovian approximation is expected\nto be valid. The method can be extended in principle to include\nnon-Markovian effects.\n\nEnd quote.\n\nThis kind of research is so analogous to my "dynamical quantization"\nidea. Men, I wish in the future people can find a quantum gravity theory\nin which it can show how quantum spacetime cohere and decohere with\nquantum entities. The incompletenss of this paper is that the coarse-grain\ntime-scale is external, otherwise it is much more analogous to idea of\ncollapsing of some level of "categorical quantization" due to measurement\nwhich is part of my "dynamical quantization" idea. The "arrow of time"\nprompts up so natural in their setting with their "pointer observables".\nThey can do calculation by "dephasing" which is a property I look for in\nmy "collapsing a level of quantization in some region within a region".\n\nA while ago, I talked with some physicists about some collective\nenhancement system or collective coherance system like\namplified matter wave in Bose-Einstein condensate. We talked about\nno (thermal) information loss when they chose a convenient\nHamiltonian with which its phase space is likely reduced for N bosonic\natoms. Men, this is another part of my "dynamical quantization". I really\nwish they or some other research groups can find a quantum field theory\nsetting for quantum entanglement rather than the entanglement is input by\nhand and by experiment. The most popular tool in this condensed matter\nresearch is the mean-field theory approach which is somewhat not\nfundamental because the 4-wave mixing (the entanglement) is stipulated by\nhand. Eventhough they have a very good motivation or experimental support\nbehind it.\n\nI hope their findings will shed some light on blackhole\nthermodynamics, arrow of time, and information loss paradox from a\ndynamical quantization perspective. (Please, pardon me. I don\'t think\ninformation loss paradox is completely solved by Hawking because, maybe, I\nam not smart enough to translate his calculation if any or interpretation\ninto my dynamical quantization setting. For example, how a unitary quantum\nsystem gets entangled and how its information extracted and all these\nshould be able to express in terms of my own language. There should have a\nrelevant picture on this.)\n\n\nI hope while I am pulling all the loose ends of a big picture about a\npossible quantum theory of gravity in an analogous way, people can see the\nreasonableness behind it though the mathematical structure has not\ncompletely emerged yet. I hope the coherance effect of quantum\nspacetime/geometry can help lessen the Coloumb repulsive force of some\nquantum system. This will eventually find some practicality.\n\n\nEnd of the post.\n\nMy saying of this posting is: "A thought can go through door gaps or\nwindow gaps of a confined room, but a brain cannot radiate so much energy\nout like a classical wave. There must have some laser pulse on some\nBEC-like fluid in some region of the brain so it must be enhanced and\nhence entangled as well like EPR photons; otherwise it should be largely\nabsorbed by the environment or the information is mostly\ndetroyed/decohered by the geometry/topology of the environment."\n\n"Entanglement due to classical effect is just a plain wrong cause-effect\norder. Since there is no such quantum field theory of entanglement, it is\npretty much up to one\'s taste of subtle twisting of the interpretation of\nquantum mechanics."\n\n"When I entered a room and once started looking at some document forms in\na tax collection place, all four people are stunned by my thought almost\nimmediately. In the past, in large open areas nearby curious people tried\nto search the source of my thought out and eventually found me. Mankind\nmust have some radar detector in their head. Which two or multiple parts\nof brain can coherently decode message?"\n\nCharles Hui\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Mon, 20 Dec 2004, Arnold Neumaier wrote:
> Mike Stay wrote:
>> In general, quantum systems don't decohere into mixtures of energy
>> eigenstates. Sometimes it's position eigenstates, sometimes some
>> other basis. I've heard the term "master equation" used in connection
>> with determining which is the preferred basis for a given system. Can
>> someone explain what one is, and how it works?
>
> A quantum master equation is a dynamical equation for the density matrix
> of a dissipative quantum systems, which approximates a quantum system
> weakly coupled to an environment at time scales long compared to the
> typical interaction time but short enough to avoid recurrence effects.
> More precisely, the dynamics is given by a completely positive Markovian
> semigroup in a representation named after Lindblad, wo discovered its
> general form.
>
> For details, see, e.g., http://www.arxiv.org/abs/cond-mat/0011204 or http://www.arxiv.org/abs/gr-qc/9406054
Abstract from http://www.arxiv.org/abs/cond-mat/0011204:
A central problem in the theory of the dynamics of open quantum systems is
the derivation of a rigorous and computationally tractable master equation
for the reduced system density matrix. Most generally, the evolution of an
open quantum system is described by a completely positive linear map. We
show how to derive a completely positive Markovian master equation (the
Lindblad equation) from such a map by a coarse graining procedure. We
provide a novel and explicit recipe for calculating the coefficients of
the master equation, using perturbation theory in the weak-coupling limit.
The only parameter external to our theory is the coarse-graining
time-scale. We illustrate the method by explicitly deriving the master
equation for the spin-boson model. The results are evaluated for the
exactly solvable case of pure dephasing, and an excellent agreement is
found within the timescale where the Markovian approximation is expected
to be valid. The method can be extended in principle to include
non-Markovian effects.
End quote.
This kind of research is so analogous to my "dynamical quantization"
idea. Men, I wish in the future people can find a quantum gravity theory
in which it can show how quantum spacetime cohere and decohere with
quantum entities. The incompletenss of this paper is that the coarse-grain
time-scale is external, otherwise it is much more analogous to idea of
collapsing of some level of "categorical quantization" due to measurement
which is part of my "dynamical quantization" idea. The "arrow of time"
prompts up so natural in their setting with their "pointer observables".
They can do calculation by "dephasing" which is a property I look for in
my "collapsing a level of quantization in some region within a region".
A while ago, I talked with some physicists about some collective
enhancement system or collective coherance system like
amplified matter wave in Bose-Einstein condensate. We talked about
no (thermal) information loss when they chose a convenient
Hamiltonian with which its phase space is likely reduced for N bosonic
atoms. Men, this is another part of my "dynamical quantization". I really
wish they or some other research groups can find a quantum field theory
setting for quantum entanglement rather than the entanglement is input by
hand and by experiment. The most popular tool in this condensed matter
research is the mean-field theory approach which is somewhat not
fundamental because the 4-wave mixing (the entanglement) is stipulated by
hand. Eventhough they have a very good motivation or experimental support
behind it.
I hope their findings will shed some light on blackhole
thermodynamics, arrow of time, and information loss paradox from a
dynamical quantization perspective. (Please, pardon me. I don't think
information loss paradox is completely solved by Hawking because, maybe, I
am not smart enough to translate his calculation if any or interpretation
into my dynamical quantization setting. For example, how a unitary quantum
system gets entangled and how its information extracted and all these
should be able to express in terms of my own language. There should have a
relevant picture on this.)
I hope while I am pulling all the loose ends of a big picture about a
possible quantum theory of gravity in an analogous way, people can see the
reasonableness behind it though the mathematical structure has not
completely emerged yet. I hope the coherance effect of quantum
spacetime/geometry can help lessen the Coloumb repulsive force of some
quantum system. This will eventually find some practicality.
End of the post.
My saying of this posting is: "A thought can go through door gaps or
window gaps of a confined room, but a brain cannot radiate so much energy
out like a classical wave. There must have some laser pulse on some
BEC-like fluid in some region of the brain so it must be enhanced and
hence entangled as well like EPR photons; otherwise it should be largely
absorbed by the environment or the information is mostly
detroyed/decohered by the geometry/topology of the environment."
"Entanglement due to classical effect is just a plain wrong cause-effect
order. Since there is no such quantum field theory of entanglement, it is
pretty much up to one's taste of subtle twisting of the interpretation of
quantum mechanics."
"When I entered a room and once started looking at some document forms in
a tax collection place, all four people are stunned by my thought almost
immediately. In the past, in large open areas nearby curious people tried
to search the source of my thought out and eventually found me. Mankind
must have some radar detector in their head. Which two or multiple parts
of brain can coherently decode message?"
Charles Hui
Kwok Man Hui
Dec25-04, 12:13 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>High quality marinade (Teriyaki and garlic perhaps)\n1 inch cubes of tender meat, preferably from the nursery\nOnions\nbell peppers\nWooden or metal skewers\n\nMarinate the meat overnight.\nGet the grill good and hot while placing meat, vegetables, and\nfruit such as pineapples or cherries on the skewers.\nDon?t be afraid to use a variety of meats.\nGrill to medium rare,\nserve with garlic cous-cous and sautéed asparagus.\nCoffee and sherbet for desert then walnuts, cheese, and port.\nCigars for the gentlemen (and ladies if they so desire)!\n\n\n\nCrock-Pot Crack Baby\n\nWhen the quivering, hopelessly addicted crack baby succumbs to death,\nget him immediately butchered and into the crock-pot, so that any\nremaining toxins will not be fatal. But don?t cook it too long,\nbecause like Blowfish, there is a perfect medium between the poisonous\nand the stimulating. Though it may not have the same effect on your\nguests, a whole chicken cooked in this fashion is also mighty tasty.\n\n1 newborn - cocaine addicted, freshly expired, cleaned and butchered\nCarrots\nonions\nleeks\ncelery\nbell pepper\npotatoes\nSalt\npepper\ngarlic, etc\n4 cups water\n\nCut the meat into natural pieces and brown very well in olive oil,\nremove, then brown half of the onions, the bell pepper, and celery.\nWhen brown, mix everything into the crock-pot,\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>High quality marinade (Teriyaki and garlic perhaps)
1 inch cubes of tender meat, preferably from the nursery
Onions
bell peppers
Wooden or metal skewers
Marinate the meat overnight.
Get the grill good and hot while placing meat, vegetables, and
fruit such as pineapples or cherries on the skewers.
Don?t be afraid to use a variety of meats.
Grill to medium rare,
serve with garlic cous-cous and sautéed asparagus.
Coffee and sherbet for desert then walnuts, cheese, and port.
Cigars for the gentlemen (and ladies if they so desire)!
Crock-Pot Crack Baby
When the quivering, hopelessly addicted crack baby succumbs to death,
get him immediately butchered and into the crock-pot, so that any
remaining toxins will not be fatal. But don?t cook it too long,
because like Blowfish, there is a perfect medium between the poisonous
and the stimulating. Though it may not have the same effect on your
guests, a whole chicken cooked in this fashion is also mighty tasty.
1 newborn - cocaine addicted, freshly expired, cleaned and butchered
Carrots
onions
leeks
celery
bell pepper
potatoes
Salt
pepper
garlic, etc
4 cups water
Cut the meat into natural pieces and brown very well in olive oil,
remove, then brown half of the onions, the bell pepper, and celery.
When brown, mix everything into the crock-pot,
Kwok Man Hui
Dec25-04, 02:59 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>SIDS: delicious in winter, comparable to old fashioned Beef and Vegetable Soup.\nIts free, you can sell the crib, baby clothes, toys, stroller... and so easy to\nprocure if such a lucky find is at hand (just pick him up from the crib and\nhe?s good to go)!\n\nSIDS victim, cleaned\n½ cup cooking oil\nCarrots\nonions\nbroccoli\nwhole cabbage\nfresh green beans\npotato\nturnip\ncelery\ntomato\n½ stick butter\n1 cup cooked pasta (macaroni, shells, etc.)\n\nRemove as much meat as possible, cube, and brown in hot oil.\nAdd a little water, season, then add the carcass.\nSimmer for half an hour keeping the stock thick.\nRemove the carcass and add the vegetables slowly to the stock,\nso that it remains boiling the whole time.\nCover the pot and simmer till vegetables are tender\n(2 hours approximately).\nContinue seasoning to taste.\nBefore serving, add butter and pasta,\nserve piping with hot bread and butter.\n\n\n\nOffspring Rolls\n\nSimilar to Vietnamese style fried rolls, they have lots of meat\n(of course this can consist of chicken, beef, pork, or shrimp).\nWho can resist this classic appetizer; or light lunch served with\na fresh salad? Versatility is probably this recipe?s greatest virtue,\nas one can use the best part of a prime, rare, yearling, or the\nmorticians occasional horror: a small miracle stopped short by a\ndrunk driver, or the innocent victim of a drive-by shooting...\n\n2 cups finely chopped very\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>SIDS: delicious in winter, comparable to old fashioned Beef and Vegetable Soup.
Its free, you can sell the crib, baby clothes, toys, stroller... and so easy to
procure if such a lucky find is at hand (just pick him up from the crib and
he?s good to go)!
SIDS victim, cleaned
½ cup cooking oil
Carrots
onions
broccoli
whole cabbage
fresh green beans
potato
turnip
celery
tomato
½ stick butter
1 cup cooked pasta (macaroni, shells, etc.)
Remove as much meat as possible, cube, and brown in hot oil.
Add a little water, season, then add the carcass.
Simmer for half an hour keeping the stock thick.
Remove the carcass and add the vegetables slowly to the stock,
so that it remains boiling the whole time.
Cover the pot and simmer till vegetables are tender
(2 hours approximately).
Continue seasoning to taste.
Before serving, add butter and pasta,
serve piping with hot bread and butter.
Offspring Rolls
Similar to Vietnamese style fried rolls, they have lots of meat
(of course this can consist of chicken, beef, pork, or shrimp).
Who can resist this classic appetizer; or light lunch served with
a fresh salad? Versatility is probably this recipe?s greatest virtue,
as one can use the best part of a prime, rare, yearling, or the
morticians occasional horror: a small miracle stopped short by a
drunk driver, or the innocent victim of a drive-by shooting...
2 cups finely chopped very
The notion of "environment induced superselection rule" offers an explanation for the problem of preferred basis. The general criteria for the observing a specified basis for the system say position, is that observable must commute with the interaction Hamiltonian of the system.
You can check Zurek's papers for more detailed information.
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