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On Moore-Read states

Posted by Raoul Santachiara

at May 12, 2009

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Raoul Santachiara is a stuff member at Laboratoire de Physique Theorique et Modeles Statistiques, Universite de Paris-Sud. His interests include statistical and mathematical physics, critical phenomena, disordered systems and entanglement properties of many-body systems. Dmitry.

I always find quite exciting when fundamental (and sometime abstract) results of pure mathematics and quantum field theory can be directly related to condensed matter or statistical mechanics problems with a clear physical interpretation and motivation. For instance, in our recent paper on “Clustering properties, Jack polynomials and unitary conformal field theories” (arXiv:0904.3702), we study the relation between the characterization of a class of symmetric polynomials with particular analytical properties (the clustering properties, specified later) and the correlation function of conserved currents in 2D massless quantum field theories, the so-called conformal field theories. The results we obtained have been directly inspired and motivated by the study of non-Abelian states in Fractional Quantum Hall systems (FQH).

The basics of FQH have been discussed extensively in many posts. In this respect I mention the post of Zlatko Papic which makes a nice introduction to the use of trial many-body wave functions in FQH. Among these functions, he introduces the Moore-Read states which represent the paradigm for non-Abelian states.

In this post I would like to start from discussing more in details some properties of the Moore-Read trial wave-functions. These are described by the so-called Pfaffian state and represent the simplest realization of pairing between spin polarized electrons.

Consider the polynomial of the complex variables z_i :

$\Psi_{Pf}(\{ z_i \})=\mbox{Pf}(\frac{1}{z_i-z_j})\prod_{i<j}(z_i-z_j)$ .

The above function is a Moore-Read state describing bosons at filling fraction $\nu=1$ . To see this, it is convenient to consider the system on a sphere with a radial magnetic field generating a flux $N_{\phi}$ . The position of -th particle on the sphere can then be represented as a complex variable z_i which is its stereographic projection. Each particle in the lowest Landau level (LLL) has orbital angular momentum $N_{\phi}/2$ and the single-particle basis state take, besides an unimportant geometric factor, the form z^m , where is the L_z angular momentum quantum number. The total flux is $N_{\phi}=N-2$ .

One can easily verify that the function $\Psi_{Pf}(\{ z_i \})$ satisfies the following clustering properties: let Z=z_1=z_2 be the position where, say, the particles and meet; the $\Psi_{Pf}(\{ z_i \})$ vanishes as (Z-z_i)^2 when the third particle approaches. Because of this simple property, one can show that the Moore-Read states is the zero-energy ground state of a three-body projection Hamiltonian. This Hamiltonian is believed to capture the physics of the LLL where the effective hamiltonian is reduced to the interaction between particles. A natural generalization of the Moore-Read states is obtained by looking for symmetric polynomials which vanishes when at least k+1 particles approach at the same point. This yields the series of the so-called Z_k Read-Rezayi states which describe bosons at filling fraction $\nu=k/2$ .

Now, the crucial observation is that symmetric polynomials with such properties can be generated by correlation functions of certain conformal field theories (CFTs). Roughly speaking, the approach of the conformal field theory is to compute correlation functions (of a 2D massless quantum field theory) by studying the infinite constraints imposed by the conformal symmetry and by, more in general, other infinite additional symmetries. From the Noether theorem at each symmetry it is associated a set conserved current which act as a generator of this symmetry. These currents generate an algebra whose representations form the Hilbert space of the theory.

Among the different families of CFTs, a central role in condensed matter is played by the so-called parafermionic theories which are CFT with an additional Z_k symmetry. Because of the particular form of the symmetry algebra, it turns out that the current correlation functions can be used to generate the polynomials with clustering properties. The simplest realization of these parafermionic theories produces the Z_k Read-Rezayi states. Note that the connection between FQH/CFT Model is a key point to understand the non-Abelian states as much of the theory underlying these is based on the monodromy properties of the CFT conformal blocks.

After the success of the series of the Z_k Read-Rezayi states, there has been an intense activity to scan the other natural direction of generalizing these states. We have seen that the symmetric polynomials associated to the Z_k Read-Rezayi states vanishes as $(Z-z_{k+1})^2$ when the k+1 particles approaches. Now, what happen if now the symmetric polynomials with clustering properties vanishes more generally as $(Z-z_{k+1})^r$ , integer? This has a direct clear physical interpretation as you are imposing that any cluster of k+1 particles has relative angular momentum less than . These states will then describe bosons at filling fraction $\nu=k/r$ .

As said above, the problem of generating such polynomials put in communication two different domains of research: from one side, the classification of well defined parafermionic theories, from the other side the theory of symmetric polynomials spanned by Jack polynomials with negative parameter.

In our paper we have investigated the interplay between these two approaches, putting in evidence some unexpected properties and proposing possible candidate for new non-abelian states… I hope that with this post I attired your attention to give a look at it!

To know more:

1. S.H. Simon, E.H. Rezayi, and N.R. Cooper, Phys. Rev. B 75, 075318 (2007).

2. B.A. Bernevig and F.D.M. Haldane, Phys. Rev. Lett. 100, 246802 (2008).

3. Vl.S. Dotsenko, J.L. Jacobsen and R. Santachiara, Nucl.Phys. B 656 259-324 (2003); Nucl.Phys. B 664 477-511 (2003); Nucl.Phys. B 679 464-494 (2004); Phys.Lett. B 584 186-191 (2004).

Condensed Matter, Journal club, Master Mason

93. Second order hydrodynamic coefficients in some field theories (like QCD)

228. Book review: D. Yoshioka. The quantum Hall effect

Jim Simons and C.N. Yang interviewed by Bill Zimmerman

198. Fractional quantum Hall effect – a few words about theory

Fermionic Schwinger-Keldysh propagators from AdS/CFT

Posted by Gregory Giecold

at May 11, 2009

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Gregory Giecold is a PhD student at CEA, Saclay. Dmitry.

In this post I will describe recent work on fermionic Schwinger-Keldysh propagators from AdS/CFT. For further details and references see ArXiv: 0904.4869.

A formulation of the AdS/CFT correspondence relates correlators of a quantum field theory at strong coupling to the boundary behaviour of bulk classical supergravity fields in an asymptotically AdS background. For spinor bulk fields and fermionic dual operators, the prescription is embedded in the relation

$\left\langle \exp\left[ \int d^{d}x \left( \bar{\chi}_0 \mathcal{O} + \bar{\mathcal{O}} \chi_0 \right) \right] \right\rangle_{QFT}=\mathcal{Z}_{SUGRA}[\chi_0, \bar{\chi}_0]$ ,

where $\chi_0=\lim_{r \rightarrow \infty} r^{d – \Delta} \Psi$ and $\Delta$ is the scaling dimension of $\mathcal{O}$ , related to the mass of the bulk spinor. The boundary lies at $r \rightarrow \infty$ . The early prescription yields Euclidean correlators. In many circumstances standard Feynman diagrams and S-matrices calculations are not adapted. In non-equilibrium settings, interactions cannot be discarded or switched adiabatically or the system might be unstable. All in all, it’s generally not possible to find an asymptotic state and use the LSZ reduction formula. The initial state is known though, so that $\langle in \mid in \rangle$ matrix elements still provide valuable data. On top of that, some systems such as the quark-gluon plasma and condensed matter models are at strong coupling. It would be of interest to find a way of obtaining real-time correlators from AdS/CFT.

But let us first review the Schwinger-Keldysh formalism for real-time propagators in quantum field theory. The Schwinger-Keldysh prescription provides a way to study real-time Green functions by considering a contour in the complexified time plane. Fields “live” on this contour. In some sense, quantum dynamics does the doubling of the degrees of freedom required for describing non-equilibrium states. Alternatively, one could view this forward-backward closed time contour as a way to introduce a fake doubled Fock space. Initial states are defined on the product of the true Fock space and the twin Fock space. A state-vector prescription has been forged for systems which are described by a density matrix (that’s the case of systems at finite temperature, out of equilibrium, etc.). The action underlying a microscopic description of the system, along with the partition functions are now split according to contributions from the four parts of the time contour, with sources $\eta_i$ and fields $\Upsilon_i$ .

Schwinger-Keldysh contour

This way, contour-ordered Green functions are mapped into a matrix

$i G(j,k)=\frac{1}{i^2} \frac{\delta^2 \ln Z\left[ \eta_{1,2}, \bar{\eta}_{1,2} \right] }{\delta \eta_j \delta \eta^{\dagger}_k}=$
$=i\begin{pmatrix}G_{11} & G_{12} \\{}G_{21} & G_{22}\\ \end{pmatrix}$ .

In the operator formalism

$G_{11}(t,\mathbf{x})=– i \langle T \Upsilon(t,\mathbf{x}) \Upsilon^{\dagger}(0) \rangle$ ,
$G_{12}(t,\mathbf{x})=\pm i \langle \Upsilon^{\dagger}(0) \Upsilon (t,\mathbf{x}) \rangle$ ,
$G_{21} (t,\mathbf{x})=– i \langle \Upsilon (t,\mathbf{x}) \Upsilon^{\dagger}(0) \rangle$ ,
$G_{22}(t,\mathbf{x})=– i \langle \hat{T} \Upsilon(t,\mathbf{x}) \Upsilon^{\dagger}(0) \rangle$ .

with the convention that upper signs stand for fermions and lower ones stand for fields obeying the Bose-Einstein statistics.

and $\hat{T}$ denote the time-ordering and anti-time-ordering operators.
Those Schwinger-Keldysh correlators are related to the more familiar retarded and advanced Green functions through

$G_R (x – y)=– i \theta(x^0 – y^0) \langle \left\{ \Upsilon(x), \Upsilon^{\dagger}(y) \right] \rangle$ ,
$G_A (x – y)=+ i \theta(y^0 – x^0) \langle \left\{ \Upsilon(x), \Upsilon^{\dagger}(y) \right] \rangle$ .

with the fancy notation $\left\{.,.\right]$ referring to either a commutator or an anticommutator.

Inserting a complete set of states gives the key relations, e.g., for bosons

$G_{11}(k)=\text{Re} G_R(k) + i \coth(\frac{\omega}{2T}) \text{Im} G_R(k)$ ,
$G_{12}(k)=\frac{2i e^{-(\beta – \sigma)\omega}}{1- e^{-\beta \omega}} \text{Im} G_R(k)$ ,
$G_{21}(k)=\frac{2i e^{- \sigma \omega}}{1 – e^{-\beta \omega}} \text{Im} G_R(k)$ ,
$G_{22}(k)=-\text{Re} G_R(k) + i \coth(\frac{\omega}{2T}) \text{Im} G_R(k)$ .

For fermions similar formula hold, with hyperbolic tangents, some sign changes and the Fermi-Dirac distribution starring instead.

When $\sigma=0$ , $G_{21}(k)=G^{>}(k)$ and $G_{12}(k)=G^{<}(k)$ . Since $G_{21}(k) – G_{12}(k) \mid_{\sigma=0}=2i \text{Im} G_R(k)$ , the relation

$G_R(k) – G_A(k)=G^{>}(k) – G^{<}(k)$

holds as required, whatever the quantum statistics of the field.

Now, are those Green functions directly related to some measurable quantities? From its definition, the lower Green function $G^{<}(k)$ is related to the average density of particles in the system or to some current density. One might also define a spectral density from the lower and upper Green functions. When particles in the system are interacting, one can check that $G^{>}(k)$ encodes the average transition probability when an extra particle of momentum is added. Besides, switching to retarded-advanced variables, so-called symmetric or Keldysh Green function appear as the sum of $G_{11}$ and $G_{22}$ . They are proportional to the imaginary part of the retarded propagator. Their interpretation is as correlators for stochastic forces experienced by the system.

Real-time correlators in AdS/CFT

Recall that the original prescription in AdS/CFT for finding gauge theory correlators from classical bulk supergravity fields is in Euclidean signature. However it might actually not be possible to perform an analytic continuation to find Minkowski correlators. This would require some knowledge of the Matsubara frequencies. Yet, in many cases the bulk wave equations can only be solved in some restricted frequency limit. Actually, there exists however a prescription, put forward by Son and Starinets in hep-th/0205051, for computing Minkowski signature retarded Green function in AdS/CFT. It involves a choice of in-going boundary conditions. The drawback is that this cannot be obviously generalized to higher point Green functions. So it might still be of interest to try and compute real-time correlators a la Schwinger-Keldysh in an AdS/CFT setting.

A hint on how to achieve this relies on the observation that Penrose diagrams of asymptotically AdS spacetimes with a black hole exhibit two boundaries on which dual gauge theory fields live. On the other hand, fields and Fock spaces are also doubled in the Schwinger-Keldysh formalism.

Kruskal diagram for the AdS-Schwarzschild black hole

This analogy was used by Herzog and Son, cf. hep-th/0212072. They show how the $2\times2$ matrix of two-point correlation functions for a scalar field and its fictitious partner field is reproduced from the AdS dual supergravity action.

The main idea is to study fields on the Kruskal diagram. Kruskal coordinates (usually labelled U and V) are suited to the study of space–times with horizons. The original, asymptotic observer coordinates (such as those which appear in the familiar Schwarzschild metric) behave badly at the horizon. Yet, a space-ship which would happen to cross a black hole horizon would not see anything particular, until, much later, its crew dies in awful circumstances experiencing unbearable tidal forces as they near the true singularity. This physical singularity cannot be removed by any choice of coordinates. But the fake horizon singularity of the early Schwarzschild metric does not appear any more once you switch to Kruskal coordinates. They also provide an extension to extra regions than the initial Schwarzschild metric. Those are the left and lower quadrants in the Penrose diagram pictured below. One can check that the near horizon behaviour of Fourier modes of the solutions to the scalar equation of motion can be expressed in terms of Kruskal coordinates. While initially the field equation was restricted in the right quadrant of the Penrose diagram, it can be extended to the whole diagram. Fields in the L quadrant can be viewed as the doubled fields of those of the R region, with the Schwinger-Keldysh formalism in mind. Besides, when one extends the mode functions to the complex Kruskal coordinates U and V planes, it turns out that positive–frequency solutions to the wave equation are analytic in the lower U and V complex planes. A solution is composed of only negative-frequency modes provided it is analytic in the upper U and V planes.

Only two linear combinations can be built from the modes in each quadrants which meet the above criterium on holomorphicity. These are

$\left\{\begin{array}{ll}u_o=u_{R,o} + \alpha_o u_{L,o} , \\{}u_i=u_{R,i} + \alpha_i u_{L,i}, \end{array} \right.$

where $u_{R,o}$ is an out-going solution to the wave equation which vanishes in the L quadrant. Similarly, $u_{L,i}$ is in-going and vanishes in the R region.

From the analyticity requirement, the in-going and out-going cross-connecting functions $\alpha_i$ and $\alpha_o$ are constrained to be

$\left\{\begin{array}{ll}\alpha_o=e^{\frac{\pi \omega}{2}}, \\{}\alpha_i=e^{-\frac{\pi \omega}{2}}.\end{array} \right.$

The prescription devised by Herzog and Son then consists in expanding a supergravity field in a basis of outgoing u_o and in-going u_i modes in the full Kruskal plane. The coefficients multiplying those basis functions are determined from the boundary behaviour of the field in the L and R quadrants.

For the scalar field they consider in their paper, the Bose-Einstein distribution then naturally appears. To compute real-time correlators, one finally just has to insert the mode expansion for the supergravity field back into the boundary supergravity action. The Son and Starinets prescription expressing retarded and advanced Green functions in terms of in-going and out-going solutions is called up in the process, which finally yields the Schwinger-Keldysh propagators. They obey the relations reviewed at the beginning of this post.

Given the recent interest in fermionic operators in AdS/CFT, with possible applications to condensed matter physics, how does the Herzog and Son recipe generalize to fermions? The near-horizon behaviour of solutions $\psi_{i}$ and $\psi_o$ to the Dirac equation in a AdS-Schwarzschild black hole background is such that additional $\sqrt{V}$ or $\sqrt{-U}$ factors appear as compared to the scalar field case. Given the importance of the solutions being analytic in a complexified extension of the Kruskal plane, 0904.4869 shortly reviews the theory of spinors and twistors in curved and complexified space-times mainly developed by Penrose. In particular, it appears that one can choose a basis for expanding dotted spinors $\Psi_-$ , which embodies those extra square root factors with a spinor dyad $\varsigma, \imath$ . By dotted spinor it is meant (in the AdS_5/CFT_4 case; there’s a generalization to other dimensions) the negative-chirality Weyl spinor component of a supergravity Dirac spinor $\Psi=\Psi_+ + \Psi_-$ .

Those square root factors provide the key ingredients for generating the Fermi-Dirac distribution. Let us see how this works. As for the scalar field case, the conditions that positive-frequency solutions are analytic in the lower U and V complex planes and negative-energy modes are analytic in their upper counterparts leads to the following linear combinations

$\left\{\begin{array}{ll}\psi_o=\psi_{R,o} + \beta_o \psi_{L,o}, \\{}\psi_i=\psi_{R,i} + \beta_i \psi_{L,i},\end{array} \right.$

with

$\left\{\begin{array}{ll}\beta_o=i e^{\frac{\pi \omega}{2}},\\{}\beta_i=– i e^{- \frac{\pi \omega}{2}}.\end{array} \right.$

They provide a basis for a spinor field defined over the full Kruskal plane of the AdS-Schwarzschild geometry

$\Psi_{-}(r,k)=\sum_k \left[ a(\omega, \mathbf{k}) \psi_o (k, r) + b(\omega, \mathbf{k}) \psi_i (k, r) \right]$ .

A point worth noting is that one does not have to expand the $\Psi_+$ field. Earlier work has established that the leading-order part in an expansion of this field near the boundary must be fixed. One must fix the “position” and leave the “momentum” free to vary in a set of canonically conjugate pairs given by $\bar{\chi}_0$ , the leading order part of $\bar{\Psi}_+$ near the boundary and \psi_0 , the leading-order component of $\Psi_-$ .

The coefficients $a(\omega, \mathbf{k})$ , $b(\omega, \mathbf{k})$ are determined by requiring that $\Psi_-(r,k)$ approaches $\Psi^R_-(k)$ and $\Psi^L_-(k)$ on their respective boundaries. This entails

$a(\omega, \mathbf{k}) \sqrt{-U} \mid_{r_{\partial M}} \varsigma=\frac{1}{e^{\pi \omega}+1} \left[ \Psi^R_- (k)+ e^{\frac{\pi \omega}{2}} \Psi^L_-(k) \right]$ ,
$b(\omega, \mathbf{k}) \sqrt{V} \mid_{r_{\partial M}} \imath=\frac{1}{e^{\pi \omega}+1} \left[ e^{\pi \omega} \Psi^R_-(k) - e^{\frac{\pi\omega}{2}} \Psi^L_-(k) \right]$ .

with the Fermi-Dirac distribution making its way through the algebra.

A key ingredient comes from the effect on spinor fields of time reversal from going to the R-quadrant to the L one. It must also be taken into account when considering the L quadrant part of the boundary action. When the dust settles, taking functional derivatives of the boundary action with respect to boundary R and L spinors yields the Schwinger-Keldysh correlators for a gauge dual fermionic operator. A review on how retarded fermionic propagators are defined in AdS/CFT and how the leading-order spinor components of $\Psi_+$ and $\Psi_-$ are related is best left to the references.

Open questions

In this post, we have focused on the quadratic part of the supergravity action. It would be interesting to compute higher point real-time correlators from higher order components of the action. It might also be of interest to extend to fermions the work of Skenderis and van Rees. As explained in 0902.4010 their work generalizes the Herzog, Son prescription and accounts for some subtle issues. Recently, there has been a sustained interest in fermions from theories with gravity duals. An open problem is to apply the approach exposed in this post to geometries dual to non-relativistic conformal field theories.

AdS/CFT, Journal club, Master Mason, Quantum field theory, String theory

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Two levels of irony of waterboarding

Posted by Dmitry

at May 10, 2009

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Started here systematically reading “Huffington press” – thinking that maybe it will allow me to develop my language skills a bit…

The hot topic there nowadays is waterboarding – can it be really considered torture or not? And if this is torture, is it really acceptable to use torture against enemies of the State – for the sake of getting a piece of information regarding a forthcoming terroristic act, etc. etc.?

Well, Geneva conventions forbid torture even during war times, and US signed those conventions. Also, there are many examples in the history of US when people have been put to jail (or to death ) for torturing.

But surprisingly after a bit of thinking one finds that the ultimate truth is somewhat trickier than that and may even contain several levels of irony in it (you know how much I love irony).

And here is the first level. In US militiary, spec ops have a possibility to go through so called “torture training” (as far as I understand, the training is really optional). The idea is that a trainee is subjected to some kind of “simplified” torture procedures in order to increase his psychological stability under torture (just in case – what if the person gets captured during an operation and tortured?). The “torture training” procedures are planned and preformed in a way allowing to minimize any personal injuries of the “tortured” – that is, guys don’t have their nails teared out or the trainer hits the guy’s head against the rubber (not stone) wall (lol) etc. etc., you’ve got the idea.

This was exactly the program recommended after 9-11 to use against terrorists/enemies of the state who might have provided some valuable information concerning bin Laden & Co – since “something we use during our own soldiers’ training is certainly Ok to use against enemies of the State” (although there is of course a primary difference between the situation when a “tortured” person can make a sign calling to stop the procedure and when a “tortured” person does not have this possibility).

The second level of irony is that this very program was developed on the basis of certain Chinese manuals, used by North Korean and Vietnamese torturers back in 1950s-60s. As one understands, the main goal of that “Chinese torture program” wasn’t really getting some valuable information from the tortured. Instead, the goal was to break the tortured to use him later in propaganda wars – “broken” soldiers and officers were typically featured on certain tapes where they sweared allegance to communism and condemned capitalist-imperialist pigs. That’s why torture could not really mean any injury – a turned to the dark side should have looked and sounded presentably.

In this respect, I think, liberals correctly suppose that waterboarding and other interesting practices were really used to get additional points in the propaganda war, instead of getting information.

Via Boris Ivanov.

Various

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Deflation and credit compression for dummies

Posted by Dmitry

at May 9, 2009

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The goal of this post is to explain at maximally comprehensive level why everybody on the other side of Atlantic is currently afraid of deflation.

So, here you go. We will start giving the answer to a somewhat simpler question: how do banks make money from air? Suppose you are in possession of 100000 USD. As long as you keep them in your pocket, it is clearly impossible for a bank to make a profit using your money, but then bank offers you 10% interest rate, you start feeling weak and bring your money to the bank, say, 90000 USD. What you have now is: 10000 USD cash and 90000 USD deposit in the bank (which you can use of course paying in any shop with the bank’s plastic debit card). On the other hand the bank has your 90000 USD in cash.

At this point we would like to claim that the amount of money circulating in the economy was suddenly increased by 90000 USD. Where did they come from? They came from air or, more precisely, from trust – the bank is obliged to return your 90000 USD as soon as you ask, and you believe that the bank can return them any time you want.

Naively, the situation did not change much: bank’s obligations are not yet real money. If your 90000 USD are kept in the bank’s vault, nothing indeed is changed and amount of money in the economy was not increased. But how can be there a banker who decides to keep your money in the vault? Of course, he will invest them instead somewhere – for example, by offering a credit line.

Said and done: the bank will leave some amount of cash (say, 10%) in the vault and invest remaining 90% (81000 USD of your hard earned money) in some sector of economy or offer a credit. If you come to the bank and withdraw a part of your money, 10% should be a sufficient backup, since the probability that everybody will simultaneously decide to withdraw their money is quite small.

At this point, the total amount of money in the economy indeed increases by 81000 USD. Namely, your 90000 USD in cash became:
a) 90000 USD in bank’s obligations, b) 9000 USD in the bank’s vault, c) 81000 USD in obligations of a person (say, his name is Tom) who took the credit from the bank, d) 81000 USD in Tom’s cash. The total amount of money in the public sector (you and Tom) increased in 1.81 times, and demand on the market increased correspondingly – the economy got warmed up.

The main conclusion at this step is that contemporary “money” is more like an obligation of one person to pay with the real money to another person.

Ok, I hope I was clear enough to this point because what you will see at the next step is a mathematical model of deflation The model depends on three parameters: 1) amount (or better say fraction) of cash that people always want to keep in their pockets, 2) reserve, a lowest amount of cash that bank has to keep in its vault – this is determined by law, 3) “the level of trust”, amount of money that banks are willing to invest after filling the reserve. The only possibility in this model for the bank to invest is to offer a credit to people (then, this money is deposited back to their accounts) – sorry if this is oversimplified.

Let us see the dynamics of the total amount of money in the system:

Stabilization of the total amount of money

Here, the purple line is the total amount of cash in the system, the red one is M2 (cash+bank’s obligations to return deposited cash+credit taken), X axis is time (in years), Y axis is total amount of USD (billions of dollars).

Exercise: check out what M2 means in the real world.

Suppose now that the level of trust is lowered somewhat (at t=5.0 years):

Level of trust is lowered

What happened here is that banks decided to be more cautious, to keep more money in their vaults and decrease amount of credits offered to people. On the other hand, people decide to keep more cash in their hands. At the result, M2 features quite a drop (more than 30%) – note though that the level of trust was not decreased significantly, people keep more than 60% of their money in banks and banks offer more than 80% of their cash in credits. This is what’s called deflation (or, better say, credit compression): the less the level of trust in the economy, the lower the total amount of money (M2) circulating in the economy.

Now, Bernarke says that he can solve the problem of deflation by printing more cash. Let us see what happens in our model after a single-time injecting of cash into the system:

After injecting cash M2 continues to drop

As you see, injecting helped – for a moment – but then rapid M2 decrease then continued.

Finally, what if we return the level of trust to the initial one after 10 years?

Level of trust returned to initial

As you see, M2 starts to grow very rapidly and stabilizes. The main conclusion one can make is that simply printing more money cannot resolve the crisis, what one ultimately has to do is to continue increasing the level of trust.

Via Sergey Schegloff (model and simulations are his as well)

Entered Apprentice, Fun, Markets and quantitative analysis

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Nanotechnology in space

Posted by Dmitry

at May 8, 2009

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Kim Jong Il Sorry, cannot help sharing it with you (bold below is mine):

Pyongyang, May 7 (KCNA) — A spokesman for the Korean Committee of Space Technology issued a statement on Thursday, one month after satellite Kwangmyongsong-2 started its normal operation after being put into orbit.

It says:

As already reported, scientists and technicians of the DPRK successfully put Kwangmyongsong-2, an experimental communications satellite, into orbit of space by means of carrier rocket Unha-2 on April 5 in the Tonghae Satellite Launching Ground in Hwadae County, North Hamgyong Province.

The carrier rocket has three stages and the satellite is tasked to transmit information about its performance and experimental relay communications to the earth along with melodies.

Installed in the carrier rocket and the satellite are measuring and transmitting devices including remote-controlled measuring devices and orbit measuring devices for the purpose of measuring orbit and sending information. There are on the ground such measuring devices as radar for tracking orbit and remote-controlled receiving devices.

The melodies of “Song of General Kim Il Sung” and “Song of General Kim Jong Il” sent to the earth at 470 MHz already made public and the observation of information about the satellite and the operation of such measuring devices as the radar for tracking orbit on the ground confirmed that the satellite was accurately put into orbit.

Various information sent by the satellite has been received and analyzed, the movement of the satellite changed as commanded by the control posts on the ground and a relay communications test through the satellite successfully conducted at relay communications posts in various regions.

The observation by the satellite and a control test were normally conducted despite the unidentified strong jamming done in the above-said communications frequency band, in particular.

We have accumulated a wealth of experience in the course of launching and operating the satellite and made great progress in laying a scientific and technological foundation for the launch of practical satellites in the days ahead.

Apparently, the North Korean technology is so advanced and Kwangmyongsong-2 satellite is so amazingly small, that virtually nobody else (including NASA, ESA, Russian Space Agency and JAXA) is able to find the satellite in space and enjoy listening the melodies of “Song of General Kim Il Sung” and “Song of General Kim Jong Il”.

Mood: amused

Source: Korean Cetral News Agency of DPRK.

Entered Apprentice, Fun