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Mar
08

Subquantum Information and Computation

Antony Valentini

(Submitted on 11 Mar 2002 (v1), last revised 12 Apr 2002 (this version, v2))

*"It is argued that immense physical resources - for nonlocal communication, espionage, and exponentially-fast computation - are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that 'non-quantum' or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish non-orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NP-complete problems in polynomial time)."*

http://arxiv.org/abs/quant-ph/0203049

Signal locality (aka nonlocal communication, passion at a distance, no cloning an arbitrary quantum state etc) follows from the linearity and unitarity of the Schrodinger equation for multi-particle entangled states psi(x1,x2, ... xN) in configuration space

-ihpsi,t = Hpsi

H is a linear Hermitian operator

U = e^iHt/hbar is unitary

UU* = U*U = 1

However, when there is spontaneous broken symmetry we get a time dependent Landau-Ginzburg (TDLG) equation that is nonlinear for a LOCAL order parameter PSI(x) condensate in ordinary space and generally has a non-unitary dissipative time dependence.

(-iah + b)PSI,t = H'PSI

N = e^iH't/hbar

NN* =/= 1

Therefore, signal nonlocality should happen in such a case when b =/= 0.

There is a large literature in soft-condensed matter physics for models of a and b for different complex systems.

In 2nd quantized notation

PSI(operator) = PSI(c-number condensate) + PSI(q-number)

PSI(q-number) = Sum over modes k dependent on boundary conditions ak

ak|nk> = nk^1/2|nk-1> in Fock space

etc.

Therefore the complete TDLG equation will be coupled to INCOHERENT RANDOM micro-quantum q-number noise that does obey the normal quantum rules in configuration space. The c-number ground state condensate COHERENT NON-RANDOM "signal" in ordinary space obeys a new set of rules "More is different." (P.W. Anderson).

A time dependent Ginzburg-Landau equation and its application to the problem of resistivity in the mixed state

A Schmid - Zeitschrift für Physik B Condensed Matter, 1966 - Springer

A time dependent modification of the Ginzburg-Landau equation is given which is based on the

assumption that the functional derivative of the GirLzburg-Landau free energy expression with

respect to the wave function is a generalized force in the sense of irreversible thermo- ...

Cited by 191 - Related articles - All 6 versions

Crossover from BCS to Bose superconductivity: Transition temperature and time-dependent Ginzburg-Landau theory

CAR Sá de Melo, M Randeria… - Physical review letters, 1993 - APS

... The time-dependent Ginzburg-Landau (TDGL) equation near T c is shown to describe a

damped mode in the BCS limit, and a propagating one in the Bose limit. A singular point is

identified at intermediate coupling where a simple TDGL description fails. ...

Cited by 255 - Related articles - BL Direct - All 5 versions

The onset of superconductivity in the time dependent Ginzburg-Landau theory

H Schmidt - Zeitschrift für Physik A Hadrons and Nuclei, 1968 - Springer

... Using the time dependent Ginzburg-Landau equation the fluctuation of the current density

is calculated. ... Our calculations are based on the time- dependent Ginzburg-Landau

equations. Their validity, therefore, is restricted to small frequencies. ...

Cited by 109 - Related articles - All 4 versions

Vortex motion and the Hall effect in type-II superconductors: A time-dependent Ginzburg-Landautheory approach

[PDF] from ufl.eduAT Dorsey - Physical Review B, 1992 - APS

... follows. In Sec. II the time-dependent Ginzburg-Landau equa- tions are presented

and discussed. In Sec. III we derive an equation of motion for a single vortex, starting

from the time-dependent Ginzburg-Landau equations. From ...

Cited by 127 - Related articles - BL Direct - All 8 versions

Time dependent Ginzburg-Landau equations of superconductivity

Q Tang… - Physica D: Nonlinear Phenomena, 1995 - Elsevier

ELSEVIER Physica D 88 (1995) 139166 PHYSICA Time dependent GinzburgLandau equations

of superconductivity Qi Tanga'l, S. Wangb a Department of Mathematics Purdue University, West

Lafayette, IN 47907, USA b Department of Mathematics and The Institute for Scientific, ...

Cited by 56 - Related articles - All 4 versions

Direct simulation of the time-dependent Ginzburg-Landau equation for type-II superconducting thin film: Vortex dynamics and VI characteristics

M Machida… - Physical review letters, 1993 - APS

We obtain the V-I characteristics of the type-II superconductors for thin film by numerically solving

the time-dependent Ginzburg-Landau equation coupled with the Maxwell equation in the

two-dimensional region. We observe a sequence of pulses in the time development of the ...

Cited by 40 - Related articles - BL Direct - All 4 versions

Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation

LR Keefe - Studies in Applied Mathematics, 1985 - adsabs.harvard.edu

... Abstract. The bifurcation structure and asymptotic dynamics of even, spatially periodic solutions

to the time-dependent Ginzburg-Landau equation are investigated analytically and numerically.

All solutions spring from unstable periodic modulations of a uniform wavetrain. ...

Cited by 104 - Related articles - Library Search - All 7 versions

Charge Conservation and Chemical Potentials in Time-Dependent Ginzburg-Landau Theory

TJ Rieger, DJ Scalapino… - Physical Review Letters, 1971 - APS

... obey the continuity equation. For a gapless system, Gor'kov and Eliashberg5 derived

from BCS theory a set of time-dependent local Ginzburg-Landau (GL) equations

which obey the continuity equation. Our final equations are ...

Cited by 45 - Related articles - All 4 versions

Time-dependent Ginzburg-Landau theory of nonequilibrium relaxation

K Binder - Physical Review B, 1973 - APS

... A. Time-Dependent Ginzburg-Landau (TDGL) Equation A real-valued order-parameter field

o(r, t) is assumed obeying the equation - Ts 8 _t -a (1 Tc )(r, t )+Bo3},t - Cv2?(r, t) - H (f, t). (33)

Here a, B, C, and rT are phenomenological (posi- tive) parameters; Tc is the critical ...

Cited by 54 - Related articles - All 2 versions

Time variation of the Ginzburg-Landau order parameter

E Abrahams… - Physical Review, 1966 - APS

... We use a nonequilibrium form of the Green's-function formulation of the BCS theory of

superconductivity to investigate the circumstances under which differential equations in space

and time, ie, "time-dependent Ginzburg-Landau equations," give a valid description of the space ...

Cited by 152 - Related articles - Library Search - All 8 versions

Antony Valentini

(Submitted on 11 Mar 2002 (v1), last revised 12 Apr 2002 (this version, v2))

http://arxiv.org/abs/quant-ph/0203049

Signal locality (aka nonlocal communication, passion at a distance, no cloning an arbitrary quantum state etc) follows from the linearity and unitarity of the Schrodinger equation for multi-particle entangled states psi(x1,x2, ... xN) in configuration space

-ihpsi,t = Hpsi

H is a linear Hermitian operator

U = e^iHt/hbar is unitary

UU* = U*U = 1

However, when there is spontaneous broken symmetry we get a time dependent Landau-Ginzburg (TDLG) equation that is nonlinear for a LOCAL order parameter PSI(x) condensate in ordinary space and generally has a non-unitary dissipative time dependence.

(-iah + b)PSI,t = H'PSI

N = e^iH't/hbar

NN* =/= 1

Therefore, signal nonlocality should happen in such a case when b =/= 0.

There is a large literature in soft-condensed matter physics for models of a and b for different complex systems.

In 2nd quantized notation

PSI(operator) = PSI(c-number condensate) + PSI(q-number)

PSI(q-number) = Sum over modes k dependent on boundary conditions ak

ak|nk> = nk^1/2|nk-1> in Fock space

etc.

Therefore the complete TDLG equation will be coupled to INCOHERENT RANDOM micro-quantum q-number noise that does obey the normal quantum rules in configuration space. The c-number ground state condensate COHERENT NON-RANDOM "signal" in ordinary space obeys a new set of rules "More is different." (P.W. Anderson).

A time dependent Ginzburg-Landau equation and its application to the problem of resistivity in the mixed state

A Schmid - Zeitschrift für Physik B Condensed Matter, 1966 - Springer

A time dependent modification of the Ginzburg-Landau equation is given which is based on the

assumption that the functional derivative of the GirLzburg-Landau free energy expression with

respect to the wave function is a generalized force in the sense of irreversible thermo- ...

Cited by 191 - Related articles - All 6 versions

Crossover from BCS to Bose superconductivity: Transition temperature and time-dependent Ginzburg-Landau theory

CAR Sá de Melo, M Randeria… - Physical review letters, 1993 - APS

... The time-dependent Ginzburg-Landau (TDGL) equation near T c is shown to describe a

damped mode in the BCS limit, and a propagating one in the Bose limit. A singular point is

identified at intermediate coupling where a simple TDGL description fails. ...

Cited by 255 - Related articles - BL Direct - All 5 versions

The onset of superconductivity in the time dependent Ginzburg-Landau theory

H Schmidt - Zeitschrift für Physik A Hadrons and Nuclei, 1968 - Springer

... Using the time dependent Ginzburg-Landau equation the fluctuation of the current density

is calculated. ... Our calculations are based on the time- dependent Ginzburg-Landau

equations. Their validity, therefore, is restricted to small frequencies. ...

Cited by 109 - Related articles - All 4 versions

Vortex motion and the Hall effect in type-II superconductors: A time-dependent Ginzburg-Landautheory approach

[PDF] from ufl.eduAT Dorsey - Physical Review B, 1992 - APS

... follows. In Sec. II the time-dependent Ginzburg-Landau equa- tions are presented

and discussed. In Sec. III we derive an equation of motion for a single vortex, starting

from the time-dependent Ginzburg-Landau equations. From ...

Cited by 127 - Related articles - BL Direct - All 8 versions

Time dependent Ginzburg-Landau equations of superconductivity

Q Tang… - Physica D: Nonlinear Phenomena, 1995 - Elsevier

ELSEVIER Physica D 88 (1995) 139166 PHYSICA Time dependent GinzburgLandau equations

of superconductivity Qi Tanga'l, S. Wangb a Department of Mathematics Purdue University, West

Lafayette, IN 47907, USA b Department of Mathematics and The Institute for Scientific, ...

Cited by 56 - Related articles - All 4 versions

Direct simulation of the time-dependent Ginzburg-Landau equation for type-II superconducting thin film: Vortex dynamics and VI characteristics

M Machida… - Physical review letters, 1993 - APS

We obtain the V-I characteristics of the type-II superconductors for thin film by numerically solving

the time-dependent Ginzburg-Landau equation coupled with the Maxwell equation in the

two-dimensional region. We observe a sequence of pulses in the time development of the ...

Cited by 40 - Related articles - BL Direct - All 4 versions

Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation

LR Keefe - Studies in Applied Mathematics, 1985 - adsabs.harvard.edu

... Abstract. The bifurcation structure and asymptotic dynamics of even, spatially periodic solutions

to the time-dependent Ginzburg-Landau equation are investigated analytically and numerically.

All solutions spring from unstable periodic modulations of a uniform wavetrain. ...

Cited by 104 - Related articles - Library Search - All 7 versions

Charge Conservation and Chemical Potentials in Time-Dependent Ginzburg-Landau Theory

TJ Rieger, DJ Scalapino… - Physical Review Letters, 1971 - APS

... obey the continuity equation. For a gapless system, Gor'kov and Eliashberg5 derived

from BCS theory a set of time-dependent local Ginzburg-Landau (GL) equations

which obey the continuity equation. Our final equations are ...

Cited by 45 - Related articles - All 4 versions

Time-dependent Ginzburg-Landau theory of nonequilibrium relaxation

K Binder - Physical Review B, 1973 - APS

... A. Time-Dependent Ginzburg-Landau (TDGL) Equation A real-valued order-parameter field

o(r, t) is assumed obeying the equation - Ts 8 _t -a (1 Tc )(r, t )+Bo3},t - Cv2?(r, t) - H (f, t). (33)

Here a, B, C, and rT are phenomenological (posi- tive) parameters; Tc is the critical ...

Cited by 54 - Related articles - All 2 versions

Time variation of the Ginzburg-Landau order parameter

E Abrahams… - Physical Review, 1966 - APS

... We use a nonequilibrium form of the Green's-function formulation of the BCS theory of

superconductivity to investigate the circumstances under which differential equations in space

and time, ie, "time-dependent Ginzburg-Landau equations," give a valid description of the space ...

Cited by 152 - Related articles - Library Search - All 8 versions