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Subtitles generated by robot

00:00

all right so let's begin shadow in my
teeth so this is the reason it works
with separator did help with a photo

00:26

Mikey and everybody audience and you
made a poster at our and I also
introduced some works in progress
okay so first let me start from a vision
so we have seen a lot of our studied law
at this rate then we we have similarly
curious if any any people have stabbed
you love most Peter Bowman field theory

01:03

research literature in the fan any any
mobile or can all theory so so I remove
whatever even the very simple people
what study we are simply curious the
author okay this is our motivation and
there are also some mathematical
motivation this is called a complex so

01:40

now if we start complex plane we start
from some point
then we there are mapping ha
map this point to the other point we do
this making on and on for many times
then we have and although these products
either flow through infinity or this one
will
move little bit locally inside the some

02:12

region I believe most of us have seen
this kind of plot so in this part if we
start from some point even dark in the
start region we add this other function
or many times the corner here we have
flow to infinity it is like original
when her so how many times do you add
function on this plot it was simply to

02:47

say that this pattern
function if you send another another
very beautiful but there are only two
regions the light they have a very
different behaviors so we we often put
in curious is this hello pure pure pure
mathematics any non equilibrium dynamics

03:19

in physics okay our mathematical
equation okay so the structure of these
talking at a Bollywood first I
introduced a 140 then I will give some
simple generalization to run random
range or even say a tea cosy
periodically driven
[Music]
okay let me first

03:59

Oh mentioned simply means that you drive
the system periodically in okay so what
do I mean by trying with the system in
time here I think we mean we consider a
time point here T capital T the standard
Heather are you see ft 0 0 is nothing
but the Hamiltonian density we simply

04:29

put I'm a little function at time
dependent function okay the the physical
meaning is very simple we simply
deformed Hamiltonian dedicated at the
function of time and see what happened
for this reaction okay so for the flow
panic killed simply mean the
dysfunctional have periodic period time
T similarly you can either call it
periodically or randomly using fully

05:03

modified it's how this function depend
on time okay very simple okay
so in one last month museum Kia the
warrior component of this component is a
composed of a virus or a generator
I wish since why the the well-known
alerts are Edgar
okay what I want to save that
challenging to solve this problem for
arbitrary app is very average not easy

05:36

to solve but now start from some simple
choice we start from some simple choice
of app once we can understand some
simple case then so the simple choice of
its app we have a speed have because I
mean compiled over L

06:07

as here actually the space
so why I took this form because if you
choose this kind of app you can fun the
Fourier component of the hoodie it's
composed of only three generators L 0 L
N and L minus n that's right there and
you thought about it apart well this 3
generator that form a closed
algebra which is a way to go caliber and
easier to handle

06:40

it's problem solvers because it's
problem solved in the time-independent
case independent of you yeah
it's like ok you have in the general
idea
our argument is going to to drive the

07:13

CFG with the virus or an algebra which
is evening there's no but now in the
initial effort we will drive the cfq in
the as a little algebra which is simpler
and we will see there are already
nancylou features in the union is a very
simple kind of driving there's some new
feature
vision
what do you mean by kitchen oh sorry

07:46

yeah yeah so start from a very concrete
example
okay we need to our time independent we
call it zero and it's one so it's zero
in nothing but a 20-week uniform with
the uniform have included st uniform use
bits we have open border and it's one

08:19

very simple equation which i jus that
sine square PI x over L this is Islam
works simple choice I will tell you okay
we will fix with the 2020s 0 and H 1 we
drive the system a with this one for
time period t 1 we switch to a serial
port I'm Kitty row we repeat this

08:49

procedure on data some other initial
State ok then let me tell you the result
first because now I is 0 and H 1 well
the only parameter that I can cure a
Camaro and Qi at the time period so this
diagram this diagram and the functional

09:22

TV rule and she what right so any
possible scale is there a relative
energy scale and Kyra
to lose any freedom when you fix it like
this because I could imagine that there
is a relative energy scale because mr. H

09:54

0 and H 1 okay yeah okay so it's really
possible
nothing interesting happen parameter
space but first this is zero or we found

10:45

there are two you mean what do you mean
by a given the face okay distinguish two
different face we simply spot either in
a system we found that unison graduated
in his reason but you can imagine a
grows linearly in time all the way in
this blue region the battery simply
oscillates ultimate all the way all the

11:17

way it's never curled up so we're going
to give the name of heating phase
although this is not good name because
conditioning the in conformity with
growth luggage
okay so good
you know diagram giving husk so I don't

11:55

mean I said the Omega is the same Omega
is the frequency theorem oh good oh my
gosh is not mean I've given it from the
[Music]
Omega actually depends on different
points different point Omega is not the
same diagram you mean okay people I
introduced reminisce if we change this

12:37

to some other choice I'm sure do you
like you can't carry a different of this
diagram okay the club let me show you
the different a phase diagram if that
would be the only have two phase
what is it underlying this is diagram we
have a body we have this is diverse okay
to say that it'll be technique but what
I want is to see if the calculation of
entropy essentially we are decorating

13:17

the correlated correlation function
career to function we try with the
system we can we can track how the
operator you have
so the primary operator UART when we try
the system comunitaria confirmation we
acted on the operator and we observe how
this operator move even in the complex
plane
oh we have fun of it as il-2 joining

13:47

this is operator we move on a circle or
a circle with the function we call it
out yet on the the pod period we move
along a circle its transformation very
simple why does it move rather than

14:21

spreading already choose a very special
each one yeah yeah actually I think is
wise to them but the premier term okay

15:10

nothing to do with this integral now in
a group oh so yeah the spread of the
operator is rated you oxt yeah yeah OST
is always very complicated operator if
you think in terms of the shown in the
picture it's always a very complicated
oh yeah but just hide it at a
complication in the location yeah yeah
in the space-time right we know the

15:40

locations we are sure holidays or how
the location change they made a movie
with transformation
so for each models chatter major have a
2x2 2x2 matrix which it as ever to see
matrix so now this problem it reduced it

16:11

very simply multiply different articles
in magics one by one
then you can check all the operator move
on the circle okay here there are three
panel Mobius transformation which is
which are called elliptic parabolic and
hyperbolic kind of information so the
correspond to the nakajima piece picking
these entities can be a theory some

16:46

popular the intuitive x-ray if we have
too many machines
and they take the transformation now as
a function of time we say how the
operator move on the complex plane for
the elliptic transformation this
operator be somebody ultimate ultimate
in time on a circle hyperbolic
transformation the operator reflow will

17:20

produce um it's point information we
also call by a power law behavior
oh oh you're using the you're using this
this de facto

19:23

but this one it spawns and if we never
come back who is it is a precision
okay feature if we even a few fish and
we try with the system energy we must

20:28

grow which means the system doesn't
absorb energy but in the keikyu phase
and we try with the system the system of
sub energy it's naturally in time
well that was was amazing the system
does not absorb energy a uniform way
there are two peaks in real space in the
real space actual piece which grows
naturally in time and you know another

20:59

pillar this one at least are exactly the
same the real space X this is time T the
color on Oh indeed and you try out the
system there are two energy chips
formerly system this one in the
numerical simulation based on xx this
vision we indeed we observe this

21:33

formation of energies these are two
peaks because you're driving to the side
yeah driving this each of the scientists
yeah you can't enjoy a pair of your
function f if you change provision Oh
the provision of the to keep depend on
Keros you are entering a period if you
face with the hammock pony trying to
change Allah although change so the

22:08

always to enemy peace even if I'm
driving with some analytic function no
just sign I'll here is very function
just everywhere okay it not easy to any

22:40

repeats but there are more amazing
things with two peaks first you can
follow the one keeping the Cairo the
other is aunty Carol but I mean if you
stop driving the system move in the
other direction similarly another
interesting feeling than all the
entitlements sorry if you to the crappy

23:10

they just stay in the same place yeah
they just stay in the same place they
don't change which time at all yeah what
would happen invited only observe
do you know the behavior sure yeah after
each cycle you would switch okay
another interesting feature is that all
the implements between the two kids I
mean just now that that's our system you

23:57

can mentally grow their linearly in time
we are all contributed by the two peaks
and we drive the system each cycle we
are talking the if you have hair to the
tips so this is a mile
I imagine the thesis there should be
some also like structure okay
also the driving will amplify everything
what do I mean the initial stage in

24:29

children have the ground state if you
through some operator in the in the
initial stage if driving with my
attractive political thriller spin
operator with the spin it's inspiring
each other
you could have you enjoy the system
under the two hundred Peaks
I'm not another that why I arrived at
over which are proportional to the the
component mnh-mnh bar also there we also

25:02

found some amazing religion but little
energy or the system made a proportional
to the central charge time it's Fernando
in ten dimensions so because you know in
America through the linear rate so the
totally I mean how universal our speech
our bodies and so long because killing
our we already started going
driving our final going to study Torah

25:35

as well sorry is there me a simple
reason for that image and and choke
irritation no context our mana general
vampires are and so we have heart of
truth so the fixed point if there are

26:11

fix pond the system we always know it
seemed I don't have time only two
minutes to it quickly close it clear out
the dragging simply let me tell every
dollar first care only the drive-in
there are two fifties
well the closing parity the driver there

26:49

are also two fifty this diagram but for
the purity is very interesting structure
in random driving through this I did not
get it approved almost the same as one D
understand my vision you know human
being
although in the random Germany they're
the only teaching piece this one but for

27:23

the causing all these three kisses the
city of its only depend on de only
depend on the the ignore exponent
of the product matrix okay we could
feature in a poly column pair of the
body
we still have three to face teaching
phase and in that meeting feel about it
there are some client structure evening

27:58

contra baby parrots on because they're
all trying some irregular start
straightening hang my entropy and what
do you mean by Cauchy pure dick oh good
we drive the system we carry the key
it's very cute so this diagram is like a

28:46

fearsome threat to life Star Trek movies
diagram some compassion or the wrath of
the driver try to even see of Q we have
give them the kind of a random driving
but no matter how powerful but it kind
of random twice into the system is
always a system of you always be only in
particular the you have momentum it will

29:18

always grow linearly in time for the
random driving we come true we have true
this theory mathematics called
fürstenberg
cast in Syria well what I want to
mention period
and all these book is talking about the
product I'll be random as they are then
you see magnetics there are many books I

29:52

thought many of them can be applied but
this like the most important one is from
the cerium I can't gather there's only
one place in space and you mentally will
always grow linearly time the total
energy will always grow the expiry okay
that's the end so the open mention we

30:28

have we want to work out some
generalizations I'm gonna drive because
function f which is really not a jerk
but what kind of join the system can be

30:58

cruelly down we also want to understand
a lot of review of
sehe this tell how works both works for
arbitrary yet there should be some solid
work with you and it's also interesting
to study the higher
how how many pose to compare all of this
to the say XE modem because you're
saying that Energy's being a C is
usually just a low-energy oh good

32:50

numerical simulations we cannot drive a
very very long time very short yeah yeah
can go to the slide where you wrote h h0
and which one is a very beginning
yeah you just is it possible to look
with each one so there's this formula
for each one right can I just say that

33:22

this sign is a square root of G and say
that it's the same cftc but what I am
actually doing is I'm just changing
metric and time yeah
yeah yeah India that I can send you know
the message that is visual basicnet time
direction most important why can't you
do it for any function why is it
important to design it is it was the
most well we can generalize we are

33:53

arbitrary arbitrary I'm get super CFCs
you answer the field universe you but if
what we come is with the peak is
determined by the condition of the fixed
point yeah we're in the exponent is

34:31

exponent determined by engineer

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